Recall that :
[tex]\text{ domain}((f\circ g)(x))=\text{ domain}(g(x))\cap\text{ domain}(f(g(x)))[/tex]
The function g is given by:
[tex]g(x)=\sqrt{x+5}[/tex]
Hence:
[tex]\text{ domain}(g(x))=[-5,\infty)[/tex]
Also,
[tex]\text{ domain}(f(g(x))=\:[-5,\:4)\cup\left(4,\:\infty\:\right)[/tex]
Therefore, the required domain is:
[-5, 4) ∪ (4, ∞)
.
