Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

Answer 1

\(\large\color{slate}{\displaystyle f(x)=x^3+4}\)
\(\large\color{slate}{\displaystyle g(x)=\sqrt[3]{x-4}}\)

yes, these functions are indeed inverses of each other.
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for f(g(x)) part, you need to plug in \(\sqrt[3]{x-4}\) for x, into the f(x).
for g(f(x)) part, you need to plug in \(x^3+4\) for x, into the g(x).