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

\(f(x) = x^3 + 4 \\
g(x) = \sqrt[3]{x-4} = (x-4)^{1/3}\\
f(g(x)) = (g(x))^3 + 4 = ((x-4)^{1/3})^3 + 4 = x - 4 + 4 = x
\)

Answer 2

Now you can try \(g(f(x))\) and prove it is also x.