Barber Potter
08/24/2024 · Senior High School
Given the definitions of \( f(x) \) and \( g(x) \) below, find the value of \( (f \circ g)(-4) \) \[ \begin{array}{l}f(x)=2 x^{2}+5 x+13 \\ g(x)=x+3\end{array} \]
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Step-by-step Solution
To find the value of \( (f \circ g)(-4) \), we first need to compute \( g(-4) \) and then use that result to find \( f(g(-4)) \).
1. **Calculate \( g(-4) \)**:
\[
g(x) = x + 3
\]
Substituting \( x = -4 \):
\[
g(-4) = -4 + 3 = -1
\]
2. **Now calculate \( f(g(-4)) = f(-1) \)**:
\[
f(x) = 2x^2 + 5x + 13
\]
Substituting \( x = -1 \):
\[
f(-1) = 2(-1)^2 + 5(-1) + 13
\]
Calculating each term:
- \( 2(-1)^2 = 2 \cdot 1 = 2 \)
- \( 5(-1) = -5 \)
- The constant term is \( 13 \)
Now combine these results:
\[
f(-1) = 2 - 5 + 13
\]
Simplifying:
\[
f(-1) = 2 - 5 + 13 = -3 + 13 = 10
\]
Thus, the value of \( (f \circ g)(-4) \) is:
\[
\boxed{10}
\]
Quick Answer
\( (f \circ g)(-4) = 10 \)
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