Answer :
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STEP -BY - STEP EXPLANATION
What to find?
f(g(h(x)))
Given:
[tex]\begin{gathered} f(x)=x^4+4 \\ g(x)=x-1 \\ h(x)=\sqrt[]{x} \end{gathered}[/tex]To solve the problem given, we will follow the steps below:
Step 1
Replace x by the value of h(x) in g(x).
That is;
[tex]\begin{gathered} g(x)=x-1 \\ \\ g(h(x))=\sqrt[]{x}-1 \end{gathered}[/tex]Step 2
Replace x in f(x) by g(h(x)).
[tex]\begin{gathered} f(x)=x^4+4 \\ \\ f(g(h(x)))=(\sqrt[]{x}-1)^4+4 \end{gathered}[/tex]Therefore, the solution is;
[tex]f(g(h(x)))=(\sqrt[]{x}-1)^4+4[/tex]