The given functions are
[tex]\begin{gathered} f(x)=x^2+5 \\ g(x)=\sqrt[]{x-4} \end{gathered}[/tex]
We need to find the composite function f(g(x))
Which means, replace x in f(x) by g(x)
[tex]f(g(x))=(\sqrt[]{x-4})^2+5[/tex]
Power 2 will cancel the square root
[tex]\begin{gathered} f(g(x))=x-4+5 \\ f(g(x))=x+1 \end{gathered}[/tex]
Let us find the domain of f(g(x))
Since there is no square root for a negative number, then
[tex]x-4\ge0[/tex]
Add 4 to both sides, then
[tex]\begin{gathered} x-4+4\ge0+4 \\ x\ge4 \end{gathered}[/tex]
Then the domain of f(g(x)) should be
[tex]\lbrack4,\infty)[/tex]
