Question

How do you find (f*g)(x) and (g*f)(x) and determine if the given functions are inverses of each other `f(x) = x^2 − 3` and `g(x) = sqrtx+3`?

Answer 1

To find `f(g(x)) and g(f(x))`, substitute, g(x) for x in f(x), and f(x) for x in g(x), respectively. If they are inverses, both substitutions will equal x.

Explanation:

`f(g(x)) = (sqrt(x) + 3)^2 -3`

`f(g(x)) = x + 6sqrt(x) + 9 -3`

`f(g(x)) = x + 6sqrt(x) + 6`

`g(f(x)) = sqrt(x^2 - 3) + 3`

They are not inverses, because both cases must reduce to x.