Question

If f(x) =1/9 x-2, what is f-1(x)?

Answer 1

9x+18

Explanation:

`f^(-1)` means they want you to find the inverse function of y=1/9 x-2.

The inverse is just a swapping of x and y.

People tend to remake the y part the subject again because they want to write it as a function.

Let's start:

`y=(1)/(9)x-2`

Swap x and y:

`x=(1)/(9)y-2`

Now it's time to solve for y:

Add 2 on both sides:

`x+2=(1)/(9)y`

Multiply both sides by 9:

`9(x+2)=y`

Distribute:

`9x+18=y`

So The inverse function is:

`f^(-1)(x)=9x+18`

Answer 2

f^-1(x) = 9(x+2)

Explanation:

To find the inverse function, exchange x and y and then solve for y

y = 1/9 x -2

Exchange x and y

x = 1/9 y-2

Solve for y

Add 2 to each side

x+2 = 1/9 y-2+2

x+2 = 1/9y

Multiply each side by 9

9(x+2) = 9*1/9y

9(x+2) = y

The inverse function

f^-1(x) = 9(x+2)