Answer
(a) $ f^{-1}(x)=\sqrt {x-4}$.
(b) $f$: $[0,\infty)$ and $[4,\infty)$. $f^{-1}$: $[4,\infty)$ and $[0,\infty)$.
(c) See graph.
Work Step by Step
(a) $f(x)=x^2+4, (x\ge0) \longrightarrow y=x^2+4\longrightarrow x=y^2+4\longrightarrow y=\sqrt {x-4}\longrightarrow f^{-1}(x)=\sqrt {x-4}$. Check $f(f^{-1})=x$ and $f^{-1}(f)=x$
(b) Domain and range of $f$: $[0,\infty)$ and $[4,\infty)$. Domain and range of $f^{-1}$: $[4,\infty)$ and $[0,\infty)$.
(c) See graph.