Question

algebra functions and simplifying

Answer 1

ANSWER:

$f(g(h(x)))=x^2+384x-2048\sqrt[]{x}-32(\sqrt[]{x})^3+4105$

STEP-BY-STEP EXPLANATION:

We have the following functions:

$\begin{gathered} f\mleft(x\mright)=x^4+9 \\ g\mleft(x\mright)=x-8 \\ h\mleft(x\mright)=\sqrt{x} \end{gathered}$

The first thing we will do is evaluate h (x) in g (x):

$g(h(x))=\sqrt[]{x}-8$

Now we evaluate this result in f (x)

$\begin{gathered} f(g(h(x)))=(\sqrt[]{x}-8)^4+9 \\ (\sqrt[]{x}-8)^4=\mleft(\sqrt{x}-8\mright)^2\mleft(\sqrt{x}-8\mright)^2=(x-16\sqrt[]{x}+64)\cdot(x-16\sqrt[]{x}+64)=x^2+384x-2048\sqrt[]{x}-32(\sqrt[]{x})^3+4096 \\ f(g(h(x)))=x^2+384x-2048\sqrt[]{x}-32(\sqrt[]{x})^3+4096+9 \\ f(g(h(x)))=x^2+384x-2048\sqrt[]{x}-32(\sqrt[]{x})^3+4105 \end{gathered}$