Question

I need help on this problem I don’t understand it

Answer 1

there are several ways we can get h(x) by means of the combination of f(x) and g(x), however the simpler version is likely

`\begin{cases} g(x)=\cfrac{9+x^5}{9 - x^5}\\\\ \boxed{f(x)=x^6} \end{cases} \hspace{5em}(f\circ g)(x)\implies ff( ~~ g(x) ~~ ) \\\\[-0.35em] ~\dotfill\\\\ f( ~~ g(x) ~~ )=[g(x)]^6\implies f( ~~ g(x) ~~ )=\left( \cfrac{9+x^5}{9 - x^5} \right)^6~~ = ~~h(x)`