Question

Let f(x)=x3 and g(x)=x√3.

Answer 1

$\text{Given that,}\\\\f(x) =x^3~~~ \text{and}~~ g(x) = \sqrt[3]x\\\\\\(f \circ g)(x) = f(g(x))= f\left(\sqrt[3]x \right) = \left(\sqrt[3] x \right)^3 =x \\\\(g\circ f)(x) =g(f(x)) = g(x^3) = \sqrt[3]{x^3} = x\\\\\text{Since} (f \circ g)(x) = (g \circ f) (x) ,~~ \text{f(x) and g(x) are inverses of each other.}$