In order to determine a function's inverse, solve for x and then switch the x and y.

`f(x) = 2x + 6`

Substitute y for f(x): `y = 2x + 6`

Solve for x.

`y = 2x + 6`

`y - 6 = 2x` Multiply by `1/2` to isolate x.

`1/2(y - 6) = x` Switch x and y.

`1/2(x-6) = y`

or `y = 1/2(x - 6)`

**Since `g(x) = 1/2(x-6)` then the 2 functions are inverses.**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.