Suppose \(f(x)=2x-9\) and \(g(x)=x^2+1\text{,}\) and we want to find \(f(g(x))\text{.}\) Since we donβt have a number to plug into \(g(x)\text{,}\) weβre going to take its entire formula and plug it into \(f(x)\text{:}\)
\begin{align*}
f(g(x)) \amp = f(x^2+1)\\
\amp = 2(x^2+1)-9\\
\amp = 2x^2-7
\end{align*}