Question

The function f(x) = 9x +5 is one-to-one.
Find an equation for f-'(x), the inverse function.

Answer 1

The inverse function is
`f^(-1)(x) = (x - 5)/(9)`

Explanation:

Inverse function:

Suppose we have a one-to-one function y = f(x). To find it's inverse, we exchange y and x, and then isolate y.

In this question:

`y = 9x + 5`

Exchanging x and y:

`x = 9y + 5`

Isolating y:

`9y = x - 5`

`y = (x - 5)/(9)`

`f^(-1)(x) = (x - 5)/(9)`

The inverse function is
`f^(-1)(x) = (x - 5)/(9)`