QuestionConsider the functions $f(x)=x^{3}-9$ and $g(x)=\sqrt[3]{x+9}$ (a) Find $f(g(x))$. (b) Find $g(f(x))$. (c) Determine whether the functions $f$ and $g$ are inverses of each other.

Studdy Solution
Since both $f(g(x)) = x$ and $g(f(x)) = x$, the functions $f$ and $g$ are inverses of each other.
The functions $f(x) = x^3 - 9$ and $g(x) = \sqrt[3]{x+9}$ are inverses of each other.