Answer
$-7$
Work Step by Step
We are given the functions:
$$\begin{align*}
f(x)&=2x^2+7x-2\\
g(x)&=x-6
\end{align*}$$
In order to calculate $f(g(5))$ using a graphing calculator, we perform the following steps:
$\textbf{Step 1}$: Form composition
Use $\textit{Function}$ from the $\textit{Y-Vars}$ menu. Enter $y_1=2x^2+7x-2$ and $y_2=x-6$. Then enter the quotient as $y_3=y_1(y_2)$.
$\textbf{Step 2}$: Evaluate composition
On the home screen enter $y_3(5)$ and press Enter. We get:
$$y_3(5)=-7$$
Therefore $f(g(5))=-7$.
