Answer:
thank you!
Step-by-step explanation:
Solve for x.
5x−2(x+1)=1/4
Enter your answer as a fraction in simplest form in the box.
x =
Answer:
x=3/4
Step-by-step explanation:
Answer:
X= 3/4
Step-by-step explanation:
Distribute
Combine like terms
Add 2 to both sides of the equation
Simplify
Divide both side s of the equation by the same turm
Simplify
Which of the following functions has an inverse that is NOT a function?
A) f(x) = (1/2)x - 1/2
B) f(x) = (x - 1)^3 + 2
C) f(x) = 2^x
D) f(x) = x(x - 1)
Step-by-step explanation:
Content
Functions and their inverses
We begin with a simple example.
Example
Let f(x)=2x and g(x)=x2.
Apply the function g to the number 3, and then apply f to the result:
g(3)=32andf(32)=3.
A similar thing happens if we first apply f and then apply g:
f(3)=6andg(6)=3.
It is clear that this will happen with any starting number. This is expressed as
f(g(x))g(f(x))=x,for all x=x,for all x.
The function f reverses the effect of g, and the function g reverses the effect of f. We say that f and g are inverses of each other.
As another example, we have
(x−−√3)3=xandx3−−√3=x,
for all real x. So the functions f(x)=x3 and g(x)=x−−√3 are inverses of each other.
If x≥0, then (x−−√)2=x and x2−−√=x. If x<0, then x−−√ is not defined. So the functions f(x)=x2 and g(x)=x−−√ are inverses of each other, but we need to be careful about domains. We will look at this more carefully later in this section.
Basics
In an earlier section of this module, we defined the composite of two functions h and g by (g∘h)(x)=g(h(x)).
Definitions
The zero function 0–:R→R is defined by 0–(x)=0, for all x.
The identity function id:R→R is defined by id(x)=x, for all x.
Example
Consider a function f:R→R.
Prove that
0–∘f=0–
f∘id=f
id∘f=f.
Show that f∘0– does not necessarily equal 0–.
Solution
We have (0–∘f)(x)=0–(f(x))=0, for all x, and so 0–∘f=0–.
We have (f∘id)(x)=f(id(x))=f(x), for all x, and so f∘id=f.
We have (id∘f)(x)=id(f(x))=f(x), for all x, and so id∘f=f.
Consider the function given by f(x)=2, for all x. Then f∘0–(x)=f(0–(x))=f(0)=2, and so f∘0–≠0–.
Definition
Let f be a function with both domain and range all real numbers. Then the function g is the inverse of f if
f(g(x))g(f(x))=x,for all x,and=x,for all x.
That is, f∘g=id and g∘f=id.
Notes.
Clearly, if g is the inverse of f, then f is the inverse of g.
We denote the inverse of f by f−1. We read f−1 as 'f inverse'. Note that f inverse has nothing to do with the function 1f.
Example
Let f(x)=x+2 and let g(x)=x−2. Show that f and g are inverses of each other.
Solution
We have
f(g(x))=f(x−2)=x−2+2=x,for all x(f∘g=id)
and
g(f(x))=g(x+2)=x+2−2=x,for all x(g∘f=id).
Hence, the functions f and g are inverses of each other.
Exercise 5
Find the inverse of
f(x)=x+7
f(x)=4x+5.
Example
Let f(x)=ax+b with a≠0. Find the inverse of f.
Solution
We have x=f(x)−ba, for all x. So let g(x)=x−ba. Then
f(g(x))g(f(x))=f(x−ba)=a(x−ba)+b=x=g(ax+b)=(ax+b)−ba=x,
for all x. Hence, g is the inverse of f.
Exercise 6
Show that f(x)=x5 and g(x)=x15 are inverses of each other.
Find the inverse of f(x)=x3+2.
We do not yet have a general enough concept of inverses, since x2 and x−−√ do not fit into this framework, nor do ex and logex. We will give a definition that covers these functions later in this section.
The horizontal-line test
Consider the function f(x)=x2, which has domain the reals and range A={x:x≥0}. Does f have an inverse?
The following graph shows that it does not. We have f(−2)=f(2)=4, and so f−1(4) would have to take two values, −2 and 2! Hence, f does not have an inverse.
Graph of y = x squared and the line y = 4 on the one set of axes.
This idea can be formulated as a test.
Horizontal-line test
Let f be a function. If there is a horizontal line y=c that meets the graph y=f(x) at more than one point, then f does not have an inverse.
Notes. Remember that the vertical-line test determines whether a relation is a function.
Example
Consider the function
f(x)=x3−x=(x+1)x(x−1).
Its graph is shown in the following diagram.
Graph of y = x cubed minus x.
Does f have an inverse?
Solution
The line y=0 meets the graph at three points. By the horizontal-line test, the function f does not have an inverse.
The function whose inverse does not exist is f(x) = x(x - 1)
The correct option is (D) f(x) = x(x - 1)
What is inverse of a function?An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
First, f(x)= [tex]\frac{1}{2} x -\frac{1}{2}[/tex]
let y= [tex]\frac{1}{2} x -\frac{1}{2}[/tex]
On solving for x we get a unique value
Then replace x and y.
It shows that the function have a unique value, which satisfies the condition of inverse.
Now, f(x) =[tex](x - 1)^3 + 2[/tex]
Again, solving for y we can get a cube root function which is a inverse of cube.
Hence, the inverse of [tex](x - 1)^3 + 2[/tex] exists.
Next, f(x) =[tex]2^x[/tex]
Solving for above we get logarithmic value. Log function are inverse of exponential function.
Hence, the inverse of [tex]2^x[/tex] exists.
Last, f(x)= x(x-1)
Solving for above create a square value.
The inverse of square never exist because having square root gives two value one is positive and other is negative.
Hence, the inverse of x(x-1) not exists.
Hence the function whose inverse does not exist is x(x-1).
Learn more about inverse of function here:
https://brainly.com/question/2541698
#SPJ2
The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per
year since.
Find the population at the beginning of 1994. Round to the nearest person.
Answer:
37356
Step-by-step explanation:
What is 8 units to the left of (3, -7)
Answer:
(-5,4)
Step-by-step explanation:
A recent poll in your state shows that 25% of the vehicles are SUV’s and 10% are trucks. The poll counted 5 million SUV’s. How many of the vehicles did they look at in total?
Answer:
20 million
Step-by-step explanation:
5 million SUVs are 25% of the total number of vehicles.
0.25x = 5,000,000
x = 20,000,000
Answer: 20 million
The question is an illustration of proportions.
A total of 20 million vehicles were looked into
The proportions are given as:
[tex]SUV = 25\%[/tex]
[tex]Trucks= 10\%[/tex]
Let the total number of vehicles be v.
The number of SUVs is given as 5 million.
So, we have:
[tex]SUV = 25\% \times v[/tex]
Substitute 5 million for SUV
[tex]5\ million= 25\% \times v[/tex]
Express the percentage as decimal
[tex]5\ million= 0.25 \times v[/tex]
Divide both sides of the equation by 0.25
[tex]20\ million = v[/tex]
Rewrite the equation as
[tex]v =20\ million[/tex]
Hence, 20 million vehicles were looked into
Read more about proportions at:
https://brainly.com/question/16981404
WHYYY ARE BOTS ON HERE HM HM?!
Answer:
Well it's because they want children to click there links for either tracking IP address's or just using it to bring you to another site.
Step-by-step explanation:
Mae receives $79.00 for working one 10-hour day. One day she had to stop after working 7 hours because of a doctor’s appointment. How much did she make that day? I need help
anyone have the answer?
Answer:
50.3 (rounded) I think? Could be wrong, however, it's what I got
How many 0.25 are there in 10.5?
Answer:
42
Step-by-step explanation:
to find how many 0.25 there are in 10.5 we have to divide 10.5 by 0.25
10.5÷0.25
=42
Hope this helped you- have a good day bro cya)
wHaT iS tHe AnWsEr?????????????
2,000 +300000000000000000000000000000000000
Answer:
3.0 E35
Step-by-step explanation:
Thanks.
i will give brainliest to the best answer.
Answer:
Step-by-step explanation:
The slope intercept form is like so:
y = mx + b
mx is the slope
b is the y-intercept
Now in your equation:
y = 0.25x + 2
0.25x is the slope
2 is the y-intercept
******Please help me help please help me ******
9514 1404 393
Answer:
y = 8
Step-by-step explanation:
If the variation is direct, any multiplier of the x-value will also multiply the y-value.
old value × -1 = new value
x: 4 × -1 = -4
y: -8 × -1 = 8
The new value of y is 8.
how to multiply 21 x 25 in oldschool way
-1/3(4+z)=-5/6 I need answer ASAP
Answer:
-2/3
Step-by-step explanation:
:)
Answer:
z = - 1.5Step-by-step explanation:
Given equation:
-1/3(4 + z) = -5/6Multiply both sides by - 3 and simplify;
(-3)(-1/3(4 + z)) = (-3) (-5/6) 4 + z = 5/24 + z = 2.5z = 2.5 - 4z = - 1.5How much greater is the surface area of the rectangular prism than the surface area of the cube?
A. 36 cm2
B. 33 cm2
C. 18 cm2
D. 45 cm2
Answer: 18 cm2
Step-by-step explanation: the surface area of the cube is 54 cm2 and the rectangular prism is 72 cm2 so 72 - 54 = 18
कौन-सा शब्द यौगिक है।
क. पुस्तकालय। ख. भाई की बहन। ग लंकेश
Answer:
help please............
Find the slope and y intercept of the line 3x+2y=-6
Answer:
Step-by-step explanation:
Slope - -3/2
y-intercept- (0,-3)
If f(x) is a linear function, what is the value of n?
Х
-4
f(x)
1-25
-10
-1
n
20
2
4
9
Answer:
The value of n is 5.
Step-by-step explanation:
We have been given that f(x) is a linear function and we are asked to find the value of n from the provided table.
x f(x)
-4 -25
-1 -10
n 20
First of all we will find the slope of the given using our given points (-4,-25) and (-1,-10) in slope formula.
m = y2-y1/x2-x1
Upon substituting coordinates of our given points we will get,
m = -10--25/-1--4
m = -10+25/-1+4
m = 15/3
m = 5
Since we know that the equation of a line in slope-intercept form is:
y = mx + b,where, m= Slope and b= y-intercept.
Upon substituting m = 5 in slope-intercept form of equation we will get,
y = 5x + b
Now let us find y-intercept by substituting coordinates of one point in our given line.
-10 = 5(-1) + b
-10 = -5 + b
-10 + 5 = -5 + 5 + b
-5 = b
y = 5x - 5
Now let us find value of n by substituting x = n and y = 20 in our equation.
20 = 5 * n - 5
20 + 5 = 5 * n - 5 + 5
25 = 5 * n
25/5 = 5 * n/5
5 = n
Therefore, the value of n is 5.
whats is the value of X
need help asap
Answer:
8
Step-by-step explanation:
Answer:
x= 98
First, you have to find what the third angle is so;
180-53-45=82
The third angle in 82.
A straight line is 180º. So you need to subtract 180-82 to get 98.
Step-by-step explanation:
if 8 ^ x=2 sqrt 2 find the value of x.
Answer:
[tex]{ \rm{ {8}^{x} = \sqrt{2} }} \\ \\ { \rm{ {2}^{3x} = {2}^{ \frac{1}{2} } }} \\ \\ { \rm{3x = \frac{1}{2} }} \\ \\ { \rm{x = \frac{1}{6} }}[/tex]
Consider the following two loans for P=$12,000.
Loan A: 5 year loan, annual interest rate of 5%.
Loan B: 3 year loan, annual interest rate of 8%.
Answer:
Simple interest-?
Step-by-step explanation:
P= 12000
T=5yrs
R=5%
Now,
Simple interest - PTR/100
= 12000*5*5/100
= $3000
Again,
P=12000
T=3yrs
R=8%
Now,
Simple interest - PTR/100
= 12000*3*8/100
= $2880
Hope this helps.
What is the hypotenuse? 68km 51km c
Answer:
85 km
Step-by-step explanation:
[tex]68^{2} +51^{2} =c^{2}[/tex]
4,624+2,601 = [tex]c^{2}[/tex]
7,225 =[tex]c^{2}[/tex]
Square both side and you get your answer 85km
Plz help I need help plz
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Need Kona talaga para bukas please
Answer:8
Step-by-step explanation:
Three cubes with volumes 8 cm3, 27 cm3 and 64 cm3 are glued together to form a solid figure. What the least possible surface area (cm2) of the solid figure?
Answer:
148 cm²Step-by-step explanation:
The cubes have sides of 2 cm, 3 cm and 4 cm respectively.
Their face area of the cubes is 4 cm², 9 cm² and 16 cm² respectively.
Total surface area of each cube is:
Side 2 cm - 6*(2*2) = 24 cm², Side 3 cm - 6*(3*3) = 54 cm², Side 4 cm - 6*(4*4) = 96 cm².Total of three cubes:
24 + 54 + 96 = 174 cm²When you glue the cubes together you lose an area equal to double face area of the smaller cube from the total surface area.
Possible decrease, provided full faces area covered:
2 cm cube with the other two ⇒ loss of four 2x2 faces 4*4 = 16 cm²3 cm or 4 cm cube with the other two ⇒ loss of two 3x3 and two 2x2 faces 2(9+4) = 26 cm²The least possible surface area is:
174 - 26 = 148 cm²3Cubes :
Volume = 8cm³ ==> r = 2cmVolume = 27cm³ => r = 3cmVolume = 64cm³ => r = 4cmSoo :
Volume - 1 = 6 × 2² = 6 × 4 = 24cm²
Volume - 2 = 6 × 3² = 6 × 9 = 54cm²
Volume - 3 = 6 × 4² = 6 × 16 = 96cm²
Totals = 24 + 54 + 96 = 174cm²[tex] \: [/tex]
surface area = 174 - 2(3² + 2²)
surface area = 174 - 2(9 + 4)
surface area = 174 - 2(13)
surface area = 174 - 26
serface area = 148cm²
[tex] \: [/tex]
-HayabusaBrainly
The container that holds the water for the football team is
1/2
full. After pouring in 9 gallons of water, it is 4/5 full. How many gallons can the container hold?
Answer:
45
Step-by-step explanation:
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Use logarithms to solve the equation for t. (Round your answer to two decimal places.)
2000/(1 + 6e−0.7t) = 1000
9514 1404 393
Answer:
2.56
Step-by-step explanation:
Multiply by (1+6e^(-.7t))/1000:
2000/1000 = 1 +6e^(-0.07t)
1 = 6e^(-0.07t) . . . . . . . . . subtract 1
e^(0.07t) = 6 . . . . . . . . . . multiply by e^(0.07t)
0.07t = ln(6) . . . . . . . . . take the natural log
t = ln(6)/0.07 . . . . . . . divide by the coefficient of t
t ≈ 2.55966 ≈ 2.56
given the drawing below what is the difference between angle D and angle B
Answer:
given the drawing below what is the difference between angle D and angle B
Step-by-step explanation:
Which number is not in scientific notation? (5 points)
11 ⋅ 1021
5.7 ⋅ 109
3.1 ⋅ 10−12
1.67 ⋅ 10−5
9514 1404 393
Answer:
(a) 11·10^21
Step-by-step explanation:
"Scientific notation" has a mantissa that has one digit to the left of the decimal point. The number 11·10^21 has two digits to the left of the decimal point, so is not in the form required by scientific notation.
11·10^21 is not in scientific notation
_____
It would be correctly written in scientific notation as as 1.1·10^22.
Answer:
A) 11 ⋅ 10^21
hey guys pls help me i need to submit this before 1hr .graphing an inverse function.y = 4x + 12 using the x values (-2,-1, 0, 1 and 2).
Answer:
4, 8, 12, 16, 24
Step-by-step explanation:
Replace the x with the x values starting at -2 and use the equation with the new x value.
E.g.
x = -2
y = 4 * -2 + 12
y = 4
Sorry if my explanation isn't the best.