Question

Please help me with this hard problem

Answer 1

Part 1: Finding $(g\circ h)(x)$

Note that $(g\circ h)(x)=g(h(x))$

In this case, it is $g(\sqrt{x+4})=(\sqrt{x+4})^{2}-3=x+4-3=\boxed{x+1}$

Part 2: Domain

For the domain, we need to make sure the radicand of h(x) is greater than or equal to 0, so we get $x+4 \geq 0 \longrightarrow \boxed{x \geq -4}$