Question

how do we Find functions f and g so that h(x) = (f ∘ g)(x).

Answer 1

ANSWER:

$\begin{gathered} f\left(x\right)=\sqrt{x} \\ \\ \:g\left(x\right)=-56x^2+8 \end{gathered}$

STEP-BY-STEP EXPLANATION:

We have the following function:

$\begin{gathered} h(x)=\sqrt{-56x^2+8} \\ \\ h(x)=\left(f\circ g\:\right)(x),\text{ therefore:} \\ \\ \left(f\circ g\:\right)(x)=\:\sqrt{-56x^2+8} \end{gathered}$

$\begin{gathered} \left(f\:\circ\:g\right)\left(x\right)=f\left(g\left(x\right)\right) \\ \\ f\left(g\left(x\right)\right)=\sqrt{-56x^2+8} \\ \\ g\left(x\right)=-56x^2+8 \\ \\ f\left(x\right)=\sqrt{x} \end{gathered}$