Questions: Given the definitions of (f(x)) and (g(x)) below, find the value of (f(g(2))).
(f(x)=2 x^2+x-13)
(g(x)=x-6)
Transcript text: Given the definitions of $f(x)$ and $g(x)$ below, find the value of $f(g(2))$.
\[
\begin{array}{l}
f(x)=2 x^{2}+x-13 \\
g(x)=x-6
\end{array}
\]
Solution
Solution Steps
Step 1: Evaluate \( g(2) \)
Given the function \( g(x) = x - 6 \), substitute \( x = 2 \) into the equation:
\[
g(2) = 2 - 6 = -4
\]
Step 2: Evaluate \( f(g(2)) = f(-4) \)
Given the function \( f(x) = 2x^2 + x - 13 \), substitute \( x = -4 \) into the equation:
\[
f(-4) = 2(-4)^2 + (-4) - 13
\]
\[
f(-4) = 2(16) - 4 - 13
\]
\[
f(-4) = 32 - 4 - 13
\]
\[
f(-4) = 15
\]