f: x 5 – 3x. (a) Find f(–1). (b) Find f –1(x).

Answers

Answer 1

Answer:

[tex]f(-1) = 8[/tex]

[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5 - 3x[/tex]

Required

[tex]f(-1)[/tex] and [tex]f^{-1}(x)[/tex]

Solving for f(-1)

Substitute -1 for x in [tex]f(x) = 5 - 3x[/tex]

[tex]f(-1) = 5 - 3(-1)[/tex]

[tex]f(-1) = 5 + 3[/tex]

[tex]f(-1) = 8[/tex]

Solving for [tex]f^{-1}(x)[/tex]

Let y = f(x)

[tex]y = 5 - 3x[/tex]

Interchange the position of x and y

[tex]x = 5 - 3y[/tex]

Make y the subject of formula (add 3y to both sides)

[tex]3y + x = 5 - 3y + 3y[/tex]

[tex]3y + x = 5[/tex]

Subtract x from both sides

[tex]3y + x - x = 5 - x[/tex]

[tex]3y = 5 - x[/tex]

Divide through by 3

[tex]\frac{3y}{3} = \frac{5}{3} - \frac{x}{3}[/tex]

[tex]y = \frac{5}{3} - \frac{x}{3}[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]


Related Questions

The area of a rectangle can be expressed by 2x2 – 7x – 4. If the rectangle has an
area of 45, find the positive value for x.

Answers

Answer:

7

Step-by-step explanation:

2x^2 - 7x - 4 = 45

2x^2 - 7x - 49 = 0 : subtract 45 from both sides

Quadratic formula:

  x = (7 ± sqrt(7^2 - 4*2*-49) ) / 4

  x = (7 ± sqrt(49 - -392)) / 4

  x = (7 ± sqrt(441)) / 4

  x = (7 ± 21) / 4

  x = (7 + 21) / 4 OR x = (7 - 21) / 4

  x = 28 / 4 OR x = -14 / 4

  x = 7 as it is the only positive answer

Find the value of x
A. 5.5
B. 6.6
C. 1.1
D. 8.8

Answers

The total value of x is D

Answer:

b

Step-by-step explanation:

Find a positive real number such that its square is equal to 14 times the number, increased by 240.

Answers

Answer:

Step-by-step explanation:

Let's call the "positive real number" X.

Basically, the question is  a riddle asking for the "solution" to 14x+240=x²

Figure that out, and

The answer is 24.

The correct answer is 24.

How to do this question plz answer me step by step plzz plz ​

Answers

Answer:

x=10 cm

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

x^2 + ( sqrt(200) )^2 = (sqrt(300))^2

x^2 +200 = 300

Subtract 200 from each side

x^2 +200-200 = 300-200

x^2 = 100

Take the square root of each side

sqrt(x^2) = sqrt(100)

x = 10

¿por qué no está definida la raíz de índice par de un número negativo?

Answers

Answer:

Porque se convierte en positivo cada vez que haces la raíz cuadrada.

Plz plz please answer it fast urgent

Answers

Answer - 1) -6/3

2)3/20

3)3/4

Hope this may helps you

Answer:

A.-2

B.its 3/20=0.15

C.3/4=0.75

Which of the following numbers can be expressed as decimals that terminate? 5 over 2, 4 over 5, 2 over 7, 4 over 3

Answers

Answer:

5/2, 4/5 are terminating decimals

Step-by-step explanation:

5/2 = 2.5  this is a terminating decimal

4/5 = .8 this is a terminating decimal

2/7 = .285714(repeating)  This is a repeating decimal

4/3 = 1.3(repeating)  this is a repeating decimal

Answer:

Hey There!!

4/5 and 5/2 are your answers!

Step-by-step explanation

Activity: A flagpole has cracked 1.7 m from the ground and fallen over, as if hinged. The top of the flagpole hit the ground 3 m from the base. How tall was the flagpole before it fell?

Answers

Answer:

Height of flagpole before it fell = 5.15 m

Step-by-step explanation:

Given:

Height of remain pole (p) = 1.7 m

Distance from base (b) = 3 m

Find:

Height of flagpole before it fell

Computation:

Using Pythagorean theorem

H = √ p² + b

Length of broken part = √ 1.7² + 3²

Length of broken part = √ 2.89 + 9

Length of broken part = √ 11.89

Length of broken part = 3.45 (Approx)

Height of flagpole before it fell = Length of broken part + Height of remain pole

Height of flagpole before it fell = 3.45 + 1.7

Height of flagpole before it fell = 5.15 m

hey loves, can any of you lovely people help me with this question?

Answers

Answer:

(c) the supplements of congruent angles are congruent.

Step-by-step explanation:

Since JKL and JLK are respectively the supplements of angles 3 and 4, we can use the justification

(c) the supplements of congruent angles are congruent.

Answer:

The answer will be C

Step-by-step explanation:

It will not be HL theorem nor SAS postulate so that gives you with C and D. Now D is incorrect because those angles arent complementary

Please help me.. please..

Answers

Answer:

i believe it's b

Step-by-step explanation:

i haven't seen a question like this is a while so i'm sorry if it's wrong

Answer:

B.

Step-by-step explanation:

x < 3 will be graphed as an empty circle at positive 3, with the line extending infinitely to the left of the circle.

x ≥ 5 will be graphed as a solid circle at positive 5, with the line extending infinitely to the right of the circle.

The two statements are best represented by graph B.

Hope this helps!

4.05 LC)
The graph shows y as a function of x:
y
Q
P
R
S
In which segment is the function decreasing?

A) P
B) Q
C) R
D) S

Answers

Answer:

r

Step-by-step explanation:

we know this because it is the only part of the graph that is moving downwards, meaning its decreasing. P is an example of increasing, Q is 'neutral' and s is also increasing.

There is a strong positive linear correlation between rainfall and the number of apples a tree produces.

Answers

Answer: C. Yes, this means more rainfall causes apple trees to produce more fruit.

Step-by-step explanation:

A positive correlation exists when one variable increases as the other variable increases.

Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces definitely means that increase in rainfall will increase the a production of apple fruit.Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces means that more rainfall causes apple trees to produce more fruit.

Yes, this means more rainfall causes apple trees to produce more fruit.

We have given that,

There is a strong positive linear correlation between rainfall and the number of apples a tree produces.

When does the positive correlation exist?

A positive correlation exists when one variable increases as the other variable increases.

Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces definitely means that increase in rainfall will increase the production of apple fruit. Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces means that more rainfall causes apple trees to produce more fruit.

Option C is correct.

Yes, this means more rainfall causes apple trees to produce more fruit.

To learn more about the correlation visit:

https://brainly.com/question/4219149

#SPJ2

PLS HELP !! I’ll appreciate it

In a two-column proof, what would you write in the reason column for any statement that is given to
you?

Answers

Answer:

explanation

Step-by-step explanation:

the reason for your statement is just your explanation of why you think that.

Question 7(Multiple Choice Worth 1 points)
(06.02 MC)
The radius of the cone is 5 in and y = 13 in. What is the volume of the cone in terms of n?
40nt in
43n in
O
100nt in
108n in

Answers

Hey there! I'm happy to help!

I assume that n is supposed to be π. To find the volume of a cone, you multiply the base by the height and then divide by three.

First, we find the area of the base, which is a circle. To find the area of a circle, you square the radius and multiply by π.

5²=25

And we multiply by π.

25π

Now we multiply by the height.

25π×13=325π

We divide by three.

325π/3≈108π

Therefore, the answer is 108π in.

Have a wonderful day! :D

Brian multiplied his average speed of 14.73 miles per hour by the amount of time he spent cross-country skiing. His product was 11.0475. A 2-column table with 4 rows titled Brian's Activity time (hours). Column 1 has entries hiking, mountain biking, horseback riding, cross-country skiing. Column 2 has entries 3, 1.45, 1.2, 0.75. Rounding to the nearest whole number, determine whether Brian’s product is reasonable. Round Brian’s average speed to . Round the activity time to . Was Brian’s product reasonable?

Answers

Answer:

15

1

yes

Step-by-step explanation:

took the thingy on edge 2020

Answer:

agree with the other person

Step-by-step explanation:

help me plz i will give brainlest

Answers

Answer:

32

Step-by-step explanation:

Pythagorean Theorem is a^2+b^2=c^2 and 40 is c^2 so we would do 40^2-24^2=b^2 so 1600-576 is 1024 and the square root of 1024 is 32 so b would be 32

Answer:

34

Step-by-step explanation:

Given:

a=24

c=40

Required:

b=?

Formula:

[tex]a {}^{2} + b {}^{2} = c {}^{2} [/tex]

Solution:

[tex]a {}^{2} + b {}^{2} = c {}^{2} = (24) {}^{2} + b {}^{2} = (40) {}^{2} = 576 + b {}^{2} = 1600 = b {}^{2} = 1600 - 576 = 1024 = b {}^{2} = 1024 = \sqrt{ {b}^{2} } = \sqrt{1024} = 34 [/tex]

Hope this helps ;) ❤❤❤

Help please!!!!””””””””””

Answers

1) because an isosceles triangle has two equal sides

Answer:

Step-by-step explanation:

1. Given

2. Given

3. Reflective Property

4. SAA

Maximize the objective function P = 2x + 1.5y for the feasible region shown. State the maximum value for P and the ordered pair at which the maximum value occurs.

Answers

Incomplete question. However, let's assume this are feasible regions to consider:

Points:

- (0, 100)

- (0, 125)

- (0, 325)

- (1, 200)

Answer:

Maximum value occurs at 325 at the point (0, 325)

Step-by-step explanation:

Remember, we substitute the points value for x, y in the objective function P = 2x + 1.5y.

- For point (0, 100): P= 2(0) + 1.5 (100) =150

- For point (0, 125): P= 2(0) + 1.5 (125) =187.5

For point (0, 325): P= 2(0) + 1.5 (325) = 487.5

For point (1, 200): P= 2(1) + 1.5 (200) = 302

Therefore, we could notice from the above solutions that at point (0,325) we attain the maximum value of P.

The sum of two even consecutive integers is −46. If the smaller integer is divided by 4 and the larger integer is increased by 11, what is the product of the two resulting integers? PLEASE HELP!!!

Answers

Answer is 66.

I hope it will help you:)

Answer:

= 66

Step-by-step explanation:

The two integers are -22 and -24, because they are both even and consecutive, and adding them equals -46.

-24 divided by 4 is -6, and -22 plus 11 is -11

Now all we have to do is find the product (multiply  -11 and -6)

And this gives us the answer: 66

Find the missing side. Round to the nearest tenth. Will give Brainliest.

Answers

Answer:

Answers are below.

Step-by-step explanation:

Sin θ = Opposite / Hypotenuse

Cos θ = Adjacent / Hypotenuse

Tan θ = Opposite / Adjacent

1) sin (60) = 16/x

x = 16/(sin 60)

x ≈ 18.46

2) cos (45) = x/13

13 cos(45) = x

x ≈ 9.19

3) tan (53) = 10/x

x = 10/tan(53)

x ≈ 7.54

4) tan (21) = x/12

12 tan(21) = x

x ≈ 4.61

find three examples of corporate logos. do they incorporate symmetry? if so, and what kind? your response should be 3-5 sentences long

Answers

Answer:

Symmetry is the property of an object to retain its shape even if it is turned or turned.

The three corporate logos are McDonald, Shell, Snapcaht

McDonald company logo is symmetrical and it is a reflective symmetry.

Shell logo is symmetrical and it is also reflective symmetry.

Snaphcat logo is symmetrical and it is also reflective symmetry.

Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x= y=

Answers

Answer:

x = 10 units, y = 5 units

Step-by-step explanation:

Given triangle ABC is a 30-60-90 triangle,

m∠C = 60°

By applying Sine rule in the given triangle,

Sin(60)°= [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

Sin(60)° [tex]=\frac{\text{AB}}{\text{AC}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\text{AB}}{\text{AC}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{5\sqrt{3}}{x}[/tex]

x = 10 units

Similarly, by applying Cosine rule in the given triangle,

Cos(60)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

Cos(60)° = [tex]=\frac{\text{BC}}{\text{AC}}[/tex]

[tex]\frac{1}{2}=\frac{y}{x}[/tex]

y = [tex]\frac{x}{2}[/tex]

y = 5 units

Therefore, x = 10 units and y = 5 units will be the answer.

if a mobile was sold for Rs.24408 after allowing 10% discount on the marked price and adding 13% VAT.Findthe discount amount.

Answers

Answer:

Hi, there!!!!

See explanation in pictures.

I hope it helps you...

Dan believes he can use the information given in the diagram and the SAS rule to prove the two triangles are congruent. Is he correct? Explain.

Answers

Answer:

Yes. There are two pairs of congruent sides and a pair of congruent angles. This follows the SAS rule.

How do u do this please help WILL GIVE BRAINLIEST

Answers

Answer: x = 9[tex]\sqrt{2\\}[/tex], y =18

Step-by-step explanation:

cuz

(sec A + tan A) (1 - sin A) = cos A prove​

Answers

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

(sec(A) + tan(A)) (1 - sin(A)) = cos(A)

Write secant as 1/cosine and tangent as sine/cosine:

(1 - sin(A)) (1/cos(A) + sin(A)/cos(A)) = ^?cos(A)

Put 1/cos(A) + sin(A)/cos(A) over the common denominator cos(A): 1/cos(A) + sin(A)/cos(A) = (sin(A) + 1)/cos(A):

(sin(A) + 1)/cos(A) (1 - sin(A)) = ^?cos(A)

Multiply both sides by cos(A):

(1 - sin(A)) (sin(A) + 1) = ^?cos(A)^2

(1 - sin(A)) (sin(A) + 1) = 1 - sin(A)^2:

1 - sin(A)^2 = ^?cos(A)^2

cos(A)^2 = 1 - sin(A)^2:

1 - sin(A)^2 = ^?1 - sin(A)^2

The left hand side and right hand side are identical:

Answer: (identity has been verified)

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           Hi my lil bunny!

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Let's do this step by step.

Prove that sec A ( 1 - sin A) ( sec A + tan A) = 1

Solving L.H.S

sec A ( 1 - sin A) ( sec A + tan A)

[tex]= \frac{1}{cos A} ( 1 - sin A ) ( \frac{1}{cos A} + \frac{sin A }{cos A})[/tex]

[tex]= \frac{(1 - sin A)}{cos A} ( \frac{1 + sin A }{cos A })[/tex][tex]= \frac{( 1 - sin A)( 1 + sin A)}{cos A X cos A}[/tex]

We know that [tex]( a - b) ( a + b) = a^2 - b^2[/tex]

[tex]= \frac{( 1^2 - sin^2 A)}{cos^2 A}[/tex]

[tex]= \frac{( 1 - sin^2 A)}{cos^2 A}[/tex]

[tex]= \frac{cos^2 A}{cos^2 A}[/tex]                         [tex]| cos^2 A + sin^2 A = 1 | cos^2 A = 1 - sin^2 A |[/tex][tex]1 - sin^2 A = cos^2 A[/tex]

[tex]= 1[/tex]

[tex]= R . H. S[/tex]

Thus, L.H.S = R.H.S

Hence proved.

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

5x + 9 = 5 + 3x : solve

Answers

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              Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]5x - 9 = 5 - 3x[/tex]

[tex]5x - 3x = 5 - 9[/tex]

[tex]2x = -4[/tex]

[tex]X = \frac{-4}{2} = -2[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

PLEASE HELP 30 POINTS!! What is the solution to the system of equations below? y = negative one-third x + 9 and y = two-thirds x minus 12 (21, 2) (21, –10) (–21, 16) (–21, –26)

Answers

Answer:

(21, 2)

Step-by-step explanation:

set equations equal to each other because they both equal y.

-1/3x + 9 = 2/3 x - 12

combine like terms by adding 1/3x and 12 to both sides.

21 = x

plug x in.

y = -1/3(21) + 9

y = -7 + 9

y = 2

check with other equation.

y = 2/3(21) - 12

y = 14 - 12

y = 2

solution: (21, 2)

hope this helps :)

Answer:

(21,2)

Step-by-step explanation:

took the quiz on edge

Help please!!!!!thxxxx

Answers

Answer:

144

Step-by-step explanation:

An angle of a regular pentagon is of 180(5-2)/5=108°

and that all the sides are equal so angle MNL=108/3=36

then MNK=180-MNL=180-36=144

I don't know if you understand this but it's hard to work without more points :)

what is a width of a rectangle prisim if the volume is 50046 cm 3 the hight is 7 cm and the llength is 13 cm

Answers

Answer:

2383.14286

Step-by-step explanation:

The volume of a prism is length times width times height. Since we already know the height and length of the prism, we can divide the volume of the prism by the height and length. This becomes: 50046/3 = 16682. Next we divide by 7: 16682/7 = 2383.14286. Hope this helps!

Other Questions
You make a scale drawing of a garden plot using the scale 2 in. = 17ft. If the length of a row of vegetables on the drawing is 3 in., howlong is the actual row?42.5 ft25.5 ft17 ft34 ft The speed of electromagnetic waves in a vacuum __________. The speed of electromagnetic waves in a vacuum __________. is larger for longer wavelengths is the same for all waves regardless of wavelength is the same as the speed of sound is larger for higher energies Learning Goal:To understand the use of Hooke's law for a spring.Hooke's law states that the restoring force F on a spring when it has been stretched or compressed is proportional to the displacement x of the spring from its equilibrium position. The equilibrium position is the position at which the spring is neither stretched nor compressed.Recall that Fx means that F is equal to a constant times x . For a spring, the proportionality constant is called the spring constant and denoted by k. The spring constant is a property of the spring and must be measured experimentally. The larger the value of k, the stiffer the spring.In equation form, Hooke's law can be writtenF =kx .The minus sign indicates that the force is in the opposite direction to that of the spring's displacement from its equilibrium length and is "trying" to restore the spring to its equilibrium position. The magnitude of the force is given by F=kx, where x is the magnitude of the displacement.In Haiti, public transportation is often by taptaps, small pickup trucks with seats along the sides of the pickup bed and railings to which passengers can hang on. Typically they carry two dozen or more passengers plus an assortment of chickens, goats, luggage, etc. Putting this much into the back of a pickup truck puts quite a large load on the truck springs.Part AA truck has springs for each wheel, but for simplicity assume that the individual springs can be treated as one spring with a spring constant that includes the effect of all the springs. Also for simplicity, assume that all four springs compress equally when weight is added to the truck and that the equilibrium length of the springs is the length they have when they support the load of an empty truck.A 70 kg driver gets into an empty taptap to start the day's work. The springs compress 2.4102 m . What is the effective spring constant of the spring system in the taptap?2.9x10^4Part BAfter driving a portion of the route, the taptap is fully loaded with a total of 23 people including the driver, with an average mass of 70 kg per person. In addition, there are three 15-kg goats, five 3-kgchickens, and a total of 25 kg of bananas on their way to the market. Assume that the springs have somehow not yet compressed to their maximum amount. How much are the springs compressed?Part CWhenever you work a physics problem you should get into the habit of thinking about whether the answer is physically realistic. Think about how far off the ground a typical small truck is. Is the answer to Part B physically realistic? France under Napoleon's rule might be best characterized as a:Roman-style republic.Greek-style democracy.enlightened dictatorship.reign of terror. solve the equation INCLUDE THE FORMULA x - 5 = 3 - 5x + 3x + 4 __________ is the drug administration method with the highest risk of overdose due to increased potency. A. Pawn B. Queen C. King D. Knight 1.How can you count following distance? The woman with the basket ran across the road. Select one: a. Simple b. Complex c. Compound PLEASE help me with this question ASAP!!!! One role of patriotic music in a democracy is: a. sharing information b. celebrating freedom c. practicing cultural engineering d. gaining social control You pick two students at random, one at a time. What is the probability that the second student is a sophomore, given that the first is a freshman The rule r_y-axis R_0,90 (x,y) is applied to ABC. Which triangle shows the final image? a. 1b. 2c. 3d. 4 There was a complete..... sitting at the desk. I haven't seen him before. a. familyb. stranger c. known d. connector Quadrilateral RSTQ is a parallelogram.RWhich of the following relationships must be true?O RS = ROO TQ QRO ZT ZRO ZSRR The lines shown below are parallel.if the green line has a slope of -1,what is the slope of the red line? How did the Israeli-Palestinian conflict affect Lebanon and why? A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle so that each side has a length of b. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. Bryan drives at an average speed of 60 miles per hour.At this rate, it will take him 3 hours to drive miles. the exact derivative of f(x)=x^3 at x=5