Question

Which function is the inverse of F(x) = 9x - 3?

Answer 1

Answer: Choice D

Work Shown

`f(x) = 9x-3\\\\y = 9x-3\\\\x = 9y-3\\\\x+3 = 9y\\\\9y = x+3\\\\y = (x+3)/(9)\\\\f^(-1)(x) = (x+3)/(9)\\\\`

Explanation: I replaced f(x) with y. Then I swapped x and y. The goal from there is to solve for y to get the inverse.

To confirm that we found the correct inverse, we should show that both
`f(f^(-1)(x)) = x \text{ and } f^(-1)(f(x)) = x` are true equations for the entire domain of all real numbers. I'll let the student do these confirmations.