Question

Let f(x) = (7x^3 + 18)2 and h(x) = x^2.Given that f(x) = (hºg)(x), find g(x).​

Answer 1

$\bf \begin{cases} f(x)=(7x^3+18)^2\\ f(x) = (h\circ g)(x)\\ h(x)=x^2 \end{cases}~\hspace{5em}(h\circ g)(x) = \stackrel{f(x)}{(7x^3+18)^2} \\\\\\ h(x) = x^2\implies \stackrel{(h\circ g)(x)}{h(~~g(x)~~)}=[g(x)]^2\implies h(~~g(x)~~)=\stackrel{f(x)}{(7x^3+18)^2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=7x^3+18~\hfill$