Question

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

Answer 1

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

Explanation:

We have the following function:

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