Line segment theorem states that if a line segment is bisected by another line, then the two parts of the line segment are equal.
This theorem is also known as the Midpoint Theorem. The formula for the Line Segment Theorem is A/B = C/D, where A and C are the two halves of the line segment, and B and D are the distances from the midpoint to the two endpoints of the line segment.
For example, consider a line segment AB with endpoints at A(-3, 2) and B(3, 2). The midpoint of the line segment is at (0,2). To calculate the length of each half of the line segment, we would use the distance formula and plug in the coordinates of the two endpoints and the midpoint.
For half A, the distance is d(A, M) = sqrt[(-3 - 0)^2 + (2 -2)^2] = 3.
For half C, the distance is d(M, B) = sqrt[(3 - 0)^2 + (2 -2)^2] = 3.
Therefore, A/B = 3/3 = 1 and C/D = 3/3 = 1. This confirms that the two halves of the line segment are equal in length.
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Use the diagram to find.. (Trigonometry)
Answer:
Step-by-step explanation:
b and f
What is a 7th interval?
A seventh interval is a chord that consists of a triad and the notes that form the seventh chord above the root of the chord. Unless otherwise stated, "7th chord" usually means the dominant 7th chord, i.e. major triad and minor 7th chord.
The 7th interval, simply called 'September', is the pitch difference between the root note and the 7th note of the diatonic scale.
Sounding the seventh above the root of the chord as his fourth note, along with the other three notes of the dominant chord, strengthens the "suspension" inherent in the function of the dominant chord, and the expected chord Increases mitigation of return to tonic.
So instead of playing "G-B-D" (Sol-Si-Re) as the dominant "C" (Do), we play "G-B-D-F" (Sol-Si-Re-Fa).
The harmonic power of the "7th interval" is so strong that some or all of his three other notes in the chord are omitted, allowing them to be visualized in the listener's ear .
In music theory, the minor seventh is one of two intervals spanning seven staff positions. It's the smaller of two sevenths, and it's minor because it spans ten semitones. A major seventh spans 11 degrees. For example, the interval from A to G is a minor seventh. This is because the G note is ten semitones above his A, and his seven staves from A to G. Diminished 7th and increased 7th have the same number of staves, but a different number of semitones (9 and 12 respectively).
Minor sevenths are rare in melodies (especially in openings), but more common than major sevenths. The most famous example, often used in theory classes, occurs between the first two words of the phrase "There's a place for us" in the West Side Story song "Somewhere." Another well-known example occurs between his two notes at the beginning of the introduction to the music of the main theme of Star Trek: The Original Series.
Complete Question:
What is personification class 7th?
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#4 Real World Scenario
A bird starts flying away from a
tree and goes exactly 6 miles
south. It then turns and flics
exactly 3 miles east. What is
the shortest distance it needs to
fly to return to the original
tree? If necessary, round your
answer to the nearest tenth.
The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.
what is pythagoras theorem ?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool.
given
by pythagoras theorem :-
shortest distance = [tex]c^{2} = a^{2} + b^{2} \\[/tex]
[tex]c^{2} = 6^{2} + 3^{2} \\c^{2} = 36 + 9\\c^{2} = 45\\c = 3\sqrt{5}[/tex]
The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.
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How do you find angles with AAA?
AAA triangles are impossible to solve further since there is nothing to show us the size.
The AAA triangle is a triangle in which all three angles are given, and the triangle is said to be similar to another triangle if any two of its three angles are equal to any two of its three angles.
Knowing only angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent.
There are four shortcuts that can be used to check whether two triangles are congruent.
You don't need to be familiar with all of the six corresponding parts, which include three angles and three sides.
When a triangle's three angles are known but not its sides, the answer is "AAA."
Since there is no information to indicate size, AAA triangles are impossible to solve further. We know their shape but not their size.
Hence, the AAA triangles are not solvable or difficult to find angles.
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Is 8 15 17 a right angle triangle?
No, 8 15 17 is not a right angle triangle. A right angle triangle is a triangle in which one of the three angles is equal to 90 degrees.
To determine if a triangle is a right angle triangle, we can use the Pythagorean theorem. This states that in a right angle triangle, the sum of the squares of the two shorter sides (a and b) will equal the square of the longest side (c).
In this case, the length of the sides are 8, 15 and 17. We can calculate the sum of the squares of the two shorter sides, which is 8² + 15² = 144 + 225 = 369. However, the square of the longest side (17²) is 289. Since 289 is not equal to 369, this means that 8 15 17 is not a right angle triangle.
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which of the following inequalities orders the numbers 0.1, 0.04, and 1/6 from least to greatest?
Answer:
0.04 < 0.1 < 1/6
Step-by-step explanation:
Activity
Luna I made the 3. 8 x 105 kilometers trip to the moon in 2. 16 x 10 minutes. In this activity, you will determine the average speed of Luna!
using division
Part A
Write an expression for the speed of Luna I In kilometers/minute. Represent this expression as a quotient of two numbers expressed in scientific
notation.
The average speed of Luna I is 1.78 x 10^-3 kilometers/minute.
To find the average speed of Luna I, we need to divide the total distance traveled (3.8 x 10^5 kilometers) by the total time it took to travel that distance (2.16 x 10^4 minutes). The quotient of these two numbers is 1.78 x 10^-3 kilometers/minute.
It's the ratio of distance covered to the time taken to cover that distance. The unit of speed is distance/time, which in this case is kilometers/minute. The speed of Luna I is in scientific notation, which is a way to express very large or very small numbers in a more manageable form.
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M(2,4) is the midpoint
between the points A(-2,9)
and B.
Find the coordinates of B.
The coordinates of B are (6,0).
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is given by the coordinates:
((x1 + x2) / 2, (y1 + y2) / 2)In this problem, we're given that the midpoint is (2, 4) and we need to find the coordinates of point B. Since we know the coordinates of the midpoint, we can set up the equation:
((x1 + x2) / 2, (y1 + y2) / 2) = (2, 4)We know that point A = (-2,9) is one endpoint, so we can substitute it into the equation
((-2 + x2) / 2, (9 + y2) / 2) = (2, 4)Solving for x2 and y2, we get x2 = 6 and y2 = 0 which is the coordinates of point B.
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What is the factor of x^3 2x^2 5x 6?
(x - 1) is thus a factor of f(x) = x3 - 2x2 - 5x + 6.
The factorization of x^3 2x^2 5x 6 is (x^2)(2x)(3) . This can be found by dividing x^3 2x^2 5x 6 by its prime factors.
You can also factor out x^2 from the expression x^3 2x^2 5x 6, which would leave you with x^2(x 2.5 6) or x^2(x 2.5 3)
Given that x3 - 2x2 - 5x + 6 = f(x),
We must determine the factored form of f in its entirety (x).
Consider (x - 1) as a factor (x).
Let's see if (x - 1) is a factor of f. (x).
f(1) = (1) (1)
3 - 2(1) (1)
2 - 5(1) + 6
= 1 - 2 - 5 + 6
= 6 - 6
= 0
f(1) = 0
(x - 1) is thus a factor of f(x) = x3 - 2x2 - 5x + 6.
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Please help!!!
if 7^9/7^n = 7^3 then n is ___?
Answer:
n= 6
Step-by-step explanation:
7^9/7^6 is the same as 7^9 - 7^6/ 7^9-6 but it gives you 7^3
Find (f/g)(x) for.
f(x) =
X² - 8x+16/
2 + 2x
; g(x) =
(6x)/
(x-4)
Therefore , the solution of the given problem of function comes out to be f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)
What is function?Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x such that f(x) = y, then the function is one-to-one
Here,
Given : f(x) =X² - 8x+16/2 + 2x
g(x) =(6x)/(x-4)
To find the f(g(x)) :
=> f(g(x)) = f(6x/(x-4))
=> f(6x/(x-4)) = (6x/(x-4) )^2 - 8((6x)/(x-4)) +16/2 + 2(6x)/(x-4)
=> f(6x/(x-4)) = 36[tex]x^{2}[/tex]/ ( [tex]x^{2}[/tex]+ 16 - 8x) - 36[tex]x^{2}[/tex]/(x+4) +8
=> f(6x/(x-4)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)
Therefore , the solution of the given problem of function comes out to be
f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)
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SU is a midsegment of QRT
If QR=-5v+96 and SU = 19v-38 than what is the value of X
Considering the given triangle, the information given helped to apply similar triangle principle to determine v to be 3.9
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
TS and TR , SU and QR
The solution is worked out using sides WX and XV, WY and YU
TS / TR = SU / QR
TS / TR = 1/2 since it is a mid segment
1 / 2 = (19v - 38) / (-5v + 96)
-5v + 96 = 2 * (19v - 38)
-5v + 96 = 38v - 72
96 + 72 = 38v + 5v
168 = 43v
v = 3.9
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This line plot shows the number of laps students ran in gym class.
Select the three true statements about the line plot.
OPTIONS:
Most of the students ran more than 3 laps.
None of the students ran more than 3 1/2 laps.
The same number of students ran 1 lap as ran 2 laps.
Most of the students ran 2 1/2 laps.
The greatest number of students ran 1 1/2 laps.
Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
From the line plot shown:
Total number of students = 3 + 4 + 2 + 2 + 8 + 4 + 6 + 9 = 38
Students who ran more than 3 laps = 2 + 8 + 4 + 6 + 9 = 29
Students who ran more than 2 1/2 laps = 2 + 2 + 8 + 4 + 6 + 9 = 31
Students who ran more than 3 1/2 laps = 2 + 8 + 4 + 6 + 9 = 29
Hence:
Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.
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Annie bought a brand new car for $32,000. The car is now worth $21,000.
(This is percent over change!!)
Using percentages we know that the value of a car decreases by 34% on average.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, we know that:
Annie brought a car at: $32000
Current price of the car: $21000
The decline in car percentage:
21000/32000 * 100
65.625%
⇒ 100 - 65.625 = 34.375%
Rounding off: 34%
Therefore, using percentages we know that the value of a car decreases by 34% on average.
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Complete question:
Annie bought a brand-new car for $32,000. The car is now worth $21,000.
By what percentage does the car's worth decrease?
A(3,-1); y= 1/3x +10
write an equation of the line passing through the given point that is parallel to the given line
the equation of the desired line is x = 3y + 6.
To find the equation of a line that is parallel to the given line
y = 1\3x + 10
and passes through the point (3,-1), since parallel lines have the same slope.
Therefore, the slope of the desired line is also 1\3.
Since the desired line passes through the point (3,-1), we can use the point-slope formula to write its equation:
y - (-1) = 1\{3}(x - 3)
Simplifying, we get
y + 1 = 1\ 3x - 1
Multiplying both sides by 3, we get
3y + 3 = x - 3
Adding 3 to both sides, we get
3y + 6 = x
Therefore, the equation of the desired line is x = 3y + 6.
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(X-5)-1 substitute the 9 for x and evaluate
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
The definition of a linear equation.A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.
Here,
Given : (X-5)-1
Thus,
after substituting the value of x with 9
We get,
=> (X-5) -1
=>(9-5)-1
=> 4 -1
=> 3
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
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49x+ 0.10= 117.90
I need help please
Subtract 0.1 from both sides49x+ 0.10= 117.90
49x+0.1-0.1=117.9-0.1
x=2.404
What is meant by variables?A quantity that may assume any one of a set of values. : a symbol representing a variable. : something that is variable. : a factor in a scientific experiment that may be subject to change.A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables49 x+0.1=117.9Move 0.1 to the right side49 x=117.8Divide both sides by 4949 x/49=117.8/49Simplifyx=2.40408To learn more about variables refers to:
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dont mind that i clicked on one lol but SOMONE PLEASE HELP RAHHAHAHAH
Here are the expressions that are equivalent to - 15 + 6x
What is an equivalent expression?
Expressions that are the same even if they may appear slightly different are called equivalent expressions. When you simplify equivalent expressions, they will all return the same value if you plug in the same variable value.
3(5 - 2x)
6x + (- 15)
15 + (- 6x)
The first one, -3(5-2x), can be simplified as -35+32x = -15 + 6x
The second one 6x + (- 15) is already in the same form as - 15 + 6x
The third one 15 + (- 6x) is just - 15 + 6x when you change the sign of -6x
The other expressions are not equivalent as they are not equal to - 15 + 6x
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What is the solution for the following set of equations 6x 2y 8 3x 7y 68?
The solution of the set of equations: 6x - 2y = 8; 3x + 7y = 68 is (4,8)
The problem can be solved using elimination - substitution method.
Set of equations:
6x - 2y = 8 .... (equation 1)
3x + 7y = 68 ..... (equation 2)
Divide equation 1 by 2
3x - y = 4 ..... (equation 3)
Eliminate x by substracting equation 3 from equation 2:
3x + 7y = 68
3x - y = 4 _
8y = 64
y = 64/8
y = 8
Substitute y = 8 into equation 3:
3x - 8 = 4
3x = 12
x = 12/3
x = 4
Hence, the solution is (4,8)
Your question is incomplete, but most probably your question was:
What is the solution for the following set of equations 6x - 2y = 8; 3x + 7y = 68 ?
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5 multiply by c 24-47-48 divide 24
Answer:
70
Step-by-step explanation:
nk
How do I write a system of equations
Pls help me do this i need hwlp if any one can figure if out
Considering that the quadrilateral EFGH is similar to quadrilateral IJKL the side LI is calculated to be
30.6How to find the side LIThe side LI is calculated using the concept of similar polygons. This concept allows for the sides to be proportionally equal to each other.
This implies that the factor used for any side will produce same result
let the factor be r and using side HG and JK to solve for the factor r
HG * r = JK
where
HG = 16
JK = 51
substituting the values and solving for r
HG * r = JK
16 * r = 51
r = 51/16
and HE * r = LI
where HE = 9.6
LI = 9.6 * 51/16
LI = 30.6
hence side LI = 30.6
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Consider the parent function f(x) below and graph
The exponential function formula for the parent function is found to be
[tex]f(x) = 2^x[/tex]
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The general formula to find an exponential function is [tex]f(x) = ab^x[/tex]
From the given graph, we take two points on the graph : (1,2) and (2,4)
Substituting in the above equation, taking f(x) as y
[tex]ab^1 = 2\\\\ab^2 = 4[/tex]
Solving the above equations, we get
a= 1, b=2
So the parent function [tex]f(x) = 2^x[/tex].
Now using this function we can graph [tex]f(2x), -3f(x), 2f(2x)\\[/tex].
[tex]f(2x) = 2^{2x} = 4^x\\\\-3f(x) = -3 * 2^x\\2f(2x) = 2 * 4^x[/tex]
Therefore using the Desmos, the above exponential functions are graphed.
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What graph is best for comparing two variables?
A scatter plot is the best graph for comparing two variables.
A scatter plot is a graph that uses dots to represent individual observations of two variables. It is a powerful tool for comparing two variables because it allows us to see the relationship between the two variables and how they are distributed. It also helps to identify any patterns or trends in the data, such as a positive correlation, a negative correlation, or no correlation at all.
Additionally, scatter plots allow us to see outliers, which are data points that are far away from the majority of the data points. This makes it easy to identify any extreme values that may be skewing the data and affecting the overall pattern of the graph. Overall, scatter plots are useful for identifying patterns, trends, and outliers in data sets, making it the best choice for comparing two variables.
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2-18. Frank wonders whether corresponding angles always have equal measure. For parts () through (d) below, use tracing paper to decide if corresponding angles have the same measure. Then determine if you have enough information to find the measures of x and y. If you do, find the angle measures and state the relationship .
The angles and their relationships are -
a) ∠x = 135° (corresponding angles), ∠y = 135° (vertical angles)
b) ∠y = 45° (liner pair angles), ∠x (not enough information provided)
c) ∠x = 135° (corresponding angles), ∠y = 45° (liner pair angles)
d) ∠x = 45° (liner pair angles), ∠y (not enough information provided)
What is angle pair relationship?
In Geometry, there are five fundamental angle pair relationships:
Complementary Angles
Supplementary Angles
Adjacent Angles
Linear Pair
Vertical Angles
a) In the first diagram -
∠x = ∠a as they are both corresponding angles to each other.
So, ∠x = 135°.
Similarly, ∠y = ∠x as they both are vertically opposite angles to each other.
So, ∠y = 135°.
b) In the second diagram -
∠y + ∠a =180° as they are both form a linear pair of angles.
So, ∠y = 180° - ∠a
∠y = 180° - 135°
∠y = 45°.
Now, ∠x cannot be deduced and no proper information is given in the image.
c) In the third diagram -
∠x = ∠a as they are both corresponding angles to each other.
So, ∠x = 135°.
Now, ∠y + ∠x =180° as they are both form a linear pair of angles.
So, ∠y = 180° - ∠x
∠y = 180° - 135°
∠y = 45°.
d) In the fourth diagram -
∠x + ∠a =180° as they are both form a linear pair of angles.
So, ∠x = 180° - ∠a
∠x = 180° - 135°
∠x = 45°.
Now, ∠x cannot be deduced and no proper information is given in the image.
Therefore, all the angles are and their relationships are found.
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What is the value of 7 power 2?
The correct answer to the given question is 49. To solve the given problem following steps are followed :
Step 1: 7 power 2 means 7 multiplied by itself 2 times.
Step 2: 7 times 7 is 49.
Step 3: So, the answer is 49.
Comparing two quantities that generate the same result when one is multiplied by a certain amount is known as a multiplicative comparison. Sam, for instance, has twice as many balloons as Sid does. Sid's got three balloons. Sam has two times Sid's amount of balloons. Sam has a total of 6 balloons, which is equal to 2 + 3 + 1.
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Is polynomial Y^4+4Y^2+5 have zeroes or not?
Yes, polynomial Y^4+4Y^2+5 has zeroes. Its zeroes can be found by factoring or using the quadratic formula: Y = -2 +/- sqrt(4-5) / 2 = -1 +/- sqrt(-1) / 2 = -1 +/- i/2.
[tex]Y^4+4Y^2+5[/tex]
=[tex](Y^2+1)²-3[/tex]
=([tex]\sqrt{Y^2+1-sqrt3}[/tex])([tex]\sqrt{Y^2+1+sqrt3}[/tex])
=(Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1)
=(Y+ sqrt3)(Y-sqrt3)(Y²-1)
=(Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1)
=0
Therefore the zeroes are Y=-√3, Y=1, Y=√3, Y=-1
Polynomial Y^4+4Y^2+5 is a fourth degree polynomial equation and can be solved by factoring or using the quadratic formula. To solve this equation by factoring, we need to use the difference of squares method. First, we rewrite the equation as (Y^2+1)²-3. Then we factor out the square of the binomial (Y^2+1): (Y^2+1-sqrt3)(Y^2+1+sqrt3). Next, we expand the first binomial to get (Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1). Then, we factor out the second binomial from the first two terms to get (Y+ sqrt3)(Y-sqrt3)(Y²-1). Finally, we expand the last binomial to get (Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1). This results in a product of zero, which means the equation has zeroes. The zeroes are Y=-√3, Y=1, Y=√3, and Y=-1.
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How many terms are there in the expression 7x2 5x?
There are 3 terms in expression 7[tex]x^{2}[/tex]-5x+5.
Monomials, binomials, trinomials, and polynomials are all examples of algebraic expressions in mathematics. Algebraic expressions are those that are modeled utilizing unknowable constants, coefficients, and variables. A variable can have any value because it is not fixed, unlike a constant, which has a definite value. Monomials, binomials, trinomials, and polynomials are examples of algebraic expressions that are created by combining variables and constants using arithmetic operations. Terms are the components of algebraic expressions that are separated by addition or subtraction. The type of expression—monomial, binomial, trinomial, or polynomial—depends on the number of terms.
An algebraic expression with three terms is called a trinomial.
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Jackson picked apples for his family. He picked a total of 6 pounds. He took 2
3
4
pounds to his aunt and 1
7
8
pounds to his mother. How many pounds of apples were left to give to his grandmother? Use the numbers and symbols to write an equation that represents the problem, then solve the equation. Symbols may be used more than once or not at all.
2
3
4
1
7
8
6 y + =
PLEASE HELPPPPPPPP
"17/8" pounds of apples were left to give to his grandmother.
Since we have given that
The quantity of apples he picked is given by 6.1/2⇒13/2 pounds.
The quantity of apples he picked for his aunt is given by 2.3/4⇒11/4 pounds.
The quantity of apples he picked for his mother is given by 1.5/8⇒13/8 pounds.
So, the total quantity left for his grandmother is given by
first we have to add the quality of apples he picked for his aunt and the number of apples he picked for his mother.
After subtracting from what he picked.
⇒13/2-(11/4+13/8)
⇒13/2-(22+13/8)
⇒13/2-(35/8)
⇒52-35/8
⇒17/8
Hence, 17/8 pounds are left for his grandmother.
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√≈≈≈≈≈Which of the following is a one-to-one function? y = [[2x]], y = x^2, f(x) = { 4x + 1;x < -2
The one-to-one function is obtained as f(x) = 4x + 1 which is a linear function.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
A function can either have one-to-one or many-to-one mapping.
One-to-one mapping implies unique element in the domain for each element in the range while for many-to-one mapping there are many elements in the domain for one element in the range.
The given functions are y = [2x] , y = x² and f(x) = 4x + 1 respectively.
They can be examined one by one as follows,
(a) y = [2x]
It is a greatest integer function.
At x = 1.1, y = [2 × 1.1] = [2.2] = 2
And, for x = 1.2, y = [2 × 1.2] = [2.4] = 2
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(b) y = x²
Find values of the function at two different x as,
x = -2, f(x) = (-2)² = 4
And, for x = 2, f(x) = 2² = 4.
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(c) f(x) = 4x + 1
It is a equation of a straight line.
Which implies it has different values for different values of x.
Thus, it is a one-to-one function.
Hence, out of the given functions only f(x) = 4x + 1 is one-to-one.
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