Question

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

Answer 1

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.

Answer 2

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