Question

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

f(x) = x^3 + 4 and g(x) = cube root(x - 4)

Answer 1

\(f(x) = x^3 + 4 \)

\(g(x) = \sqrt[3]{x - 4} \)

\(f(g(x)) = f(\sqrt[3]{x - 4}) \)

\( ~~~~~~~~~~~~~= ( \sqrt[3]{x - 4})^3 + 4 \)

\(~~~~~~~~~~~~~= x - 4 + 4\)

\(~~~~~~~~~~~~~ = x\)

Now try doing the same for \(g(f(x))\).

Answer 2

your job is to compute
\[f(g(x))=f(\sqrt[3]{x-4})=(\sqrt[3]{x-4})^3+4\] and see that you get \(x\)

Answer 3

oh, what @mathstudent55 said!