Question

If f(x) = x^4 + 4, g(x) = x - 1 and h(x) = √x, then f(g(h(x))) =

Answer 1

STEP -BY - STEP EXPLANATION

What to find?

f(g(h(x)))

Given:

`\begin{gathered} f(x)=x^4+4 \\ g(x)=x-1 \\ h(x)=\sqrt[]{x} \end{gathered}`

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;

`\begin{gathered} g(x)=x-1 \\ \\ g(h(x))=\sqrt[]{x}-1 \end{gathered}`

Step 2

Replace x in f(x) by g(h(x)).

`\begin{gathered} f(x)=x^4+4 \\ \\ f(g(h(x)))=(\sqrt[]{x}-1)^4+4 \end{gathered}`

Therefore, the solution is;

`f(g(h(x)))=(\sqrt[]{x}-1)^4+4`