Question

If f(x) = 1/2x-6 then what does f^-1(x) equal?

A. f^-1(x) = 2x+6

B. f^-1(x) = 2x-6

C. f^-1(x) = 2(x+6)

D. f^-1(x) = 2(x-6)


I am really asking this question because I don't understand how to change f(x) to f^-1(x).
This is just a sample problem, so you could make up your own, similar equation and help me understand. Thank you!

Answer 1

I think what you're looking for is the inverse of the function.

First, let's talk about notation:
f(x) =
`(1)/(2)`x - 6 is the same as
y =
`(1)/(2)`x - 6

To find the inverse of the function, you do the following steps.
1. write the function in terms of x and y:
y =
`(1)/(2)`x - 6
2. Rewrite this equation switching the variables x and y
x =
`(1)/(2)`y - 6
3. Solve this equation for y: y = 2(x + 6)