Question

Select the correct answer. Find the inverse of function f. f(x)=9x+7

Answer 1

If
`f^(-1)(x)` is the inverse of
`f(x)`, then by definition

`f\left(f^(-1)(x)\right) = x`

Given that
`f(x)=9x+7`, we have

`f\left(f^(-1)(x)\right) = 9f^(-1)(x)+7 = x`

Solve for
`f^(-1)(x)` :

`9f^(-1)(x) + 7 = x \\\\ 9f^(-1)(x) = x - 7 \\\\ f^(-1)(x) = \frac{x-7}9`