Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = eight divided by square root of quantity two x plus four.

Answer 1

$\bf y=f[\ g(x)\ ]=\cfrac{8}{\sqrt{2x+4}}\\\\ -------------------------------\\\\ \begin{cases} f(x)=\cfrac{8}{\sqrt{x}}\\\\ g(x)=2x+4 \end{cases}\qquad f[\ \underline{g(x)}\ ]=\cfrac{8}{\sqrt{\underline{g(x)}}}\implies f[\ \underline{g(x)}\ ]=\cfrac{8}{\sqrt{\underline{2x+4}}}$