Question

Determine if the pair of functions are inverses.

Answer 1

To determine if two functions are inverses, we have to compose the functions into each other and get a value of x.

f(g(x)) =
`3(\sqrt{(x - 12)/(3) })^(2) - 12`

The square root and the square cancel each other out.

f(g(x)) =
`3((x - 12)/(3)) - 12`

The 3's cancel each other out.

f(g(x)) = x - 12 - 12 = x - 24

since f(g(x)) = x - 24, these two functions are not inverses of each other.