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

Expert Answers

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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.

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