Answer:
To prove that g(x) and f(x) are the inverse functions of each other, we compute the compositions:
[tex]\begin{gathered} \text{For all x}\ge0 \\ (g\circ g)(x)=g(f(x))=g(x^2)=\sqrt[]{x^2}=x, \\ (f\circ g)(x)=f(g(x))=f(\sqrt[]{x})=(\sqrt[]{x})^2=x\text{.} \end{gathered}[/tex]
The graph of the functions is:
