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If f(x)=9x-8, which of the following is the inverse of f(x) *Apex*

If f(x)=9x-8, which of the following is the inverse of f(x) *Apex*-example-1

2 Answers

3 votes

Answer:

A.
f^(-1)(x)=(x+8)/(9)

Explanation:

We have been given a function
f(x)=9x-8. We are asked to find the inverse function for our given function.

First of all, we will rewrite
f(x) as
y as:


y=9x-8

To find the inverse function, we will interchange x and y variables and then solve for y.


x=9y-8

Now, we will add 8 on both sides of our given equation.


x+8=9y-8+8


x+8=9y

Switch sides:


9y=x+8

Now, we will divide both sides of our equation by 9.


(9y)/(9)=(x+8)/(9)


y=(x+8)/(9)

Now, we will replace
y with
f^(-1)(x) as:


f^(-1)(x)=(x+8)/(9)

Therefore, the inverse function for our given function would be
f^(-1)(x)=(x+8)/(9) and option A is the correct choice.

User Jingx
by
7.0k points
7 votes

Define

f(x) and y are two different ways of denoting the same thing. Thus...

f(x) = 9x - 8 is the same as y = 9x - 8

Inverse: the inverse of a function is the resulting equation when x and y switch places and the equation is solved for x

Solve

Switch the places of x and y in the given equation:

y = 9x - 8 ---> x = 9y - 8

Solve the new equation for y (isolate y on the left side of the equation)

x = 9y - 8

x + 8 = 9y - 8 + 8

x + 8 = 9y

(x + 8) / 9 = 9y / 9

(x + 8)/9 = y

y = (x + 8) / 9

y =
(x+8)/(9)

Now you have the inverse of f(x) = 9x - 8:

A)
f^(-1) =
(x + 8)/(9)

Key Terms

inverse

User Graham Leggett
by
6.2k points