show whether or not the functions are inverses of each other.

Expert Answers
baxthum8 eNotes educator| Certified Educator

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.

tonys538 | Student

Two functions f(x) and g(x) are inverse functions if the value of f(g(x)) = x.

For example consider a function f(x) = x + 2 and g(x) = x - 2

f((g(x)) = f(x - 2) = x - 2 + 2 = x

This holds for any function f(x) and its inverse `f^-1(x)` .

The value of `f(f^-1(x))` should always equal x.