Question

Find two functions fand g such that (fog)(x) = h(x). (There are f(x) and g(x).) h(x) = x2-6 (F(x), g(x)) =( 12 = 6.23

Answer 1

Weh ave the following:

They ask us to find the functions that make up h (x) knowing that:

$\begin{gathered} h(x)=\sqrt[3]{x^2-6} \\ \mleft(f\circ g\mright)\mleft(x\mright)=h(x) \end{gathered}$

Therefore:

$\begin{gathered} f(x)=\sqrt[3]{x} \\ g(x)=x^2-6 \\ \text{therefore} \\ (f\: \circ\: g)(x)=\sqrt[3]{x^2-6} \end{gathered}$

The answer is:

$(\sqrt[3]{x},x^2-6)$