Given: F(x)= 5 x - 6 and G(x)= x - 4
(FoG)^-1=

Answers

Answer 1

By definition of inverse function,

[tex]F\left(F^{-1}(x)\right) = x[/tex]

so that

[tex]5F^{-1}(x) - 6 = x[/tex]

[tex]5F^{-1}(x) = x + 6[/tex]

[tex]F^{-1}(x) = \dfrac{x + 6}5[/tex]

Similarly,

[tex]G\left(G^{-1}(x)\right) = G^{-1}(x) - 4 = x \implies G^{-1}(x) = x+4[/tex]

Then the inverse of the composition [tex]F\circ G[/tex] is such that

[tex]\left(F \circ G\right) \left((F \circ G)^{-1}(x)\right) = x[/tex]

By definition of composition,

[tex](F\circ G)(x) = F(G(x))[/tex]

Applying [tex](F\circ G)^{-1}[/tex] to this recovers x, and this involves first inverting F, then G:

[tex](F\circ G)^{-1}(x) = G^{-1}\left(F^{-1}(x)\right)[/tex]

So, we find

[tex](F\circ G)^{-1}(x) = G^{-1}\left(F^{-1}(x)\right) = G^{-1}\left(\dfrac{x+6}5\right) = \dfrac{x+6}5 + 4 = \boxed{\dfrac{x+26}5}[/tex]


Related Questions

0.000456 in scientific notation (Please answer fast this is on my final math exam!)

Answers

Answer:

0.000456 in scientific notation

= 4.56 × 10-4

Step-by-step explanation:

Can I have brainliest?

0.000456 in scientific notation is 4.56 × 10-4

1. Two students are asked to find the angle measures of AEFG, given that the triangle is isosceles. AEFG has an exterior angle at which has a measure of 110%. Their work is shown below.
Which answer is correct? Explain below.

Serin's Answer: The measure of Angle G is 70 degrees. Since the base angles are congruent, the measure of Angel F is also 70degrees.This leaves 40 degrees for Angle E.

Lam's Answer: The measure of angle G is 70degrees. Since an isosceles triangle has two congruent angles, the measure of Angle E and Angle F must be 55degrees

O Both are correct.

ONeither is correct.

Answers

Answer:

∆EFG has an exterior angle at G which has a measure of 110°. Which answer is incorrect ... Since external angle is 110 degrees, the internal is 70 degrees

Step-by-step explanation:

no problem we all get stuck

The angles can be ∠ G  = 70°, ∠ F = 70° and ∠E =  40° or ∠ G  = 70°, ∠ F = ∠ E = 55° hence both are correct so, option C is correct.

What is triangle?

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The triangle is isosceles, and AEFG has an exterior angle at which has a measure of 110°,

Calculate the interior angles of the triangle as shown below,

∠ G = 180 - 110  (exterior angle)

∠ G  = 70°

Since the remaining angles can be ∠ F = 70° and ∠E = 180 - 70 + 70 = 40°

or ∠ F = ∠ E = 55°

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write each power as a product of the same factor. Then find the value. 4^4

Answers

Answer:

256

Step-by-step explanation:

4^4 means 4raise to power 4. so, it's typically 4x4x4x4 which is 256

The Shanghai Maglev Train takes 8 minutes to travel a distance of 30.5 kilometres.

Work out the average speed of the train.

Answers

Answer:

228.75 km/h

Step-by-step explanation:

average speed = total distance / total time

The Average speed is 228.75 Km/h.

What is speed- Distance Formula?Speed = Distance/TimeDistance = Speed X Time, and Time = Distance / Speed,

Given:

Distance= 30.5 Km

Time= 8 min

       = 8/60 hr= 2/15 hour

Now, Average speed= Distance / time

                                  = 30.5 x 15/2

                                 = 228.75 Km/ h

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Do number 12 on the pic

Answers

Answer:

  $21.83

Step-by-step explanation:

The amount spent will be the difference between the starting balance and the ending balance:

  18.53 -(-3.30) = 18.53 +3.30 = 21.83

You spent $21.83 on lunch this week.

PLEASE HELPPPP !! Which points have positive y coordinates?
A) A and F
B) A and B
C) F and H
D) B and F

Answers

B is the correct answer

Liz is a salesperson at a department store. She gets paid an hourly wage plus a 5 percent commission on all her sales. Her pay is given by the formula below.

P = $6h + $0.05k

In this formula, h is the number of hours worked, and k is the dollar amount of sales. Liz worked 36 hours last week and sold $2,700 of merchandise. What was her total pay for the week?

Answers

Answer:

$351.00

Step-by-step explanation:

Our first step in this process is to find what the hours - represented by h - times $6.00 would result in. Since 36 ⋅ 6 results in $216.00, we know that $216.00 + $0.05k = last week's pay for Liz.

Our second step is to find what $0.05 is being multiplied by. We see in the given information that k represents the dollar amount of sales. Therefore, in the second step of this process, we'll be multiplying 0.05 by 2700, which results in $135.00.

We then add $216.00 - the remaining value to be added - to the second value of $135.00, making the answer to this math problem $351.00.

Hopefully this helped a bunch! And tell me if you need any further assistance. ( :

Mr smith’s Pizza parlor

Answers

The questions are not readable. try uploading a better picture.

Solve the equation or inequality. t/3+t/2−350=270

Answers

Answer:

t=744

Step-by-step explanation:

t/3+t/2-350=270 add 350 on both sides

t/3+t/2=620 convert both fractions containing t into a fraction with a common base

2t/6+3t/6 = 620 add the fractions containing t

5t/6=620 factor out the 5

5*(t/6)=620 divide both sides by 5

t/6=124 multiply both sides by 6 (note, you could have just divided 620 by 5/6 on both sides, or multiplided both sides by 6/5)

t=744

is 5/8 greater than 61%? thanks i have late stuff that i need done

Answers

Answer:

5/8 is 62.5% which makes it greater

Step-by-step explanation:

Convert the fraction to a decimal and then just multiply it with 100

5/8 is 0.625

0.625×100 is 62.5

just add a %

then you get 62.5%

Factor the following polynomial completely. x2n – y2n

Answers

Answer:

(x/y)^2n-2n

(x/y)⁰

=1

since any number raised to power of 0 is 1

What is (16x+9)+(−9x−5) ?

Answers

the awnswer is 11 hope it helps

Factor
10x + 100x + 250

Answers

10(11x+25)
Is the answer

The base of a triangle is 13 cm rounded to the nearest integer.
The perpendicular height of the triangle is 4.7 cm rounded to 1 dp.
Write the error interval for the area, a, of the triangle in the form m ≤ a < n.

Answers

Answer:

30.55 <_ a < 30.55

Step-by-step explanation:

a = 1/2 × b × h

a = 1/2 × 13 × 4.7

a = 30.55 cm^2

30.55 <_ a < 30.55

7. Write an equation for the line in slope- intercept form ​

Answers

Answer:

y equals -2x - 3

Step-by-step explanation:

hope it helps

(would appreciate mark brainliest)

Natalie is graphing point T at (1,8). should she moves to the right 8 units or up 8 units? Explain

Answers

Answer:

move 1 to the right and 8 units up

Step-by-step explanation:

The mean of 16, X, 3, 14,57 is 22. Find
Х

Answers

Answer:

20

Step-by-step explanation:

Given,

The mean of 16, X, 3, 14, 57 is 22.

Therefore,

(16+X+3+14+57)/5 = 22

(16+X+3+14+57) = 110

(90+X) = 110

X = 110-90

X = 20

The value of x will be 20.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mean of set 16, X, 3, 14, 57 is 22.

Now,

Since, The mean of 16, X, 3, 14, 57 is 22.

Hence, By definition of mean we get;

⇒ 16 + X + 3 + 14 + 57 / 5 = 22

Solve for x as;

⇒ 90 + X / 5 = 22

⇒ 90 + X = 22 × 5

⇒ 90 + X = 110

⇒ X = 110 - 90

⇒ X = 20

Thus, The value of x will be 20.

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laura's family is going on a vacation. they will drive 4,180 miles over the next two weeks. about how many miles will they drive on average each week?

Answers

Answer:

l auras family will drive 2090 miles watch week because you decide by 2 because there are 2 weeks

T
Зл
Solve for the interval <<
2
2
3. 2 cos? 0-5 cos e = 3
(it put it in wrong so i put a picture of the question)

Answers

Answer:

540 g m/s.

Step-by-step explanation:

If you bought 12.6 gallons of gasoline as $1.20 per gallon, how much did the gasoline cost?

Answers

Answer:

15.12$

Step-by-step explanation:

Gallons = 12.6

Cost = $1.20

Gasoline Cost = ??

12.6 ×1.20

=15.12

Hence, gasoline will cost 15.12 $

pls mark me as brainliest! :D

Identify if the table below shows a proportional relationship.
x
y
1
5
02
2
.
7
5
13
Proportional
Not Proportional

Answers

Answer:

i know answer i heard some were i think

what is the difference of 23xand 9 x​

Answers

Answer:

14x

Step-by-step explanation:

.....................

Solve the Equation [tex]\frac{5}{2}[/tex] · X = 1

Answers

[tex]\dfrac 52 \cdot x = 1\\\\\implies 5x = 2\\\\\implies x = \dfrac 25[/tex]

Answer:

5/2

Step-by-step explanation:

What is an equation of the line that passes through the point (-7, -6) and is
parallel to the line 2 - y = 7?

Answers

Answer:

[tex]y = -6[/tex]

Step-by-step explanation:

Because is a line is of the form

[tex]y = mx + b[/tex]

and its parallel to the line

[tex]2 - y &= 7\\- y &= 5\\y = -5[/tex]

So that's meaning that the slope [tex]m[/tex] is equal to 0 then the equation now is of the form

[tex]y = b[/tex]

Then if pass for the point -6 and [tex]b[/tex] is the point of cut with the [tex]y[/tex] axis then our equation of the line is equal to

[tex]y = -6[/tex]

Please help meeeee please please c

Answers

Answer:

the item would cost $9000

Math and Science If 7 giant solar power

plants generate 1.3 gigawatts (GW) of

energy to power 900,000 homes, how

many gigawatts can 21 giant solar plants

generate?

Answers

Answer:

Step-by-step explanation:

multiply everything by three to get your answer

Please help!!!!!!!!!!!!!

Answers

Answer:

can you also send a graph that might help rn

Step-by-step explanation:

All changes avec
7. The price of a plane ticket varies Inversely with the amount of tickets purchased at one time. If 2 plane tickets costs $350 each, how much will a ticket cost when purchasing 7 plane tickets?
O $25
O $100
O $1225
O $220

Answers

Answer:

1225

350/2=175

175 x 7 = 1225

Sort the expressions into the correct categories based on their value. Note that some expressions may not belong to any of the categories.

(help with the circled ones)

Answers

Answer:

the answer for (9squared divided by 3) - ( 3 x 5 ) = 12

Step-by-step explanation:

(9squared divided by 3) - ( 3 x 5 ) = 12

9x9 = 81

81 ÷ 3 = 27

27 - (3x5)

3 x 5 = 15

27 - 15 = 12

so it goes in the 12 box

4squared - ( 2 x 3 )

4squared = 4 x 4

4 x 4 = 16

16 - (2 x 3)

2 x 3 = 6

16 - 6 = 10

so it goes in the 10 box

PLEASE HELP.
Use the drawing tool(s) to form the correct answer on the provided graph. The graph of f(x) = x is shown on the coordinate plane. Function g is a transformation of f as shown below. g(x) = f(-2/3x)
WILL GIVE 100 POINTS.

Answers

Step-by-step explanation:

Given function:

f(x) = x

The transformation of f(x) is g(x):

g(x) = f(-2/3x) = -2/3x

The graph of g(x) is attached below

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