Question
Consider the functions \( f(x)=4-x^{2} \) and \( g(x)=3 x+5 \). Find the value of \( f(g(-2)) \). \( \begin{array}{l}5 \\ 3 \\ 1\end{array} \)
Ask by Stuart Higgins. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(g(-2)) = 3 \)
Solution
To find the value of \( f(g(-2)) \), we'll follow these steps:
1. **Calculate \( g(-2) \):**
Given \( g(x) = 3x + 5 \),
\[
g(-2) = 3(-2) + 5 = -6 + 5 = -1
\]
2. **Now, calculate \( f(g(-2)) = f(-1) \):**
Given \( f(x) = 4 - x^2 \),
\[
f(-1) = 4 - (-1)^2 = 4 - 1 = 3
\]
**Answer:** \( 3 \)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To find \( f(g(-2)) \), we first need to compute \( g(-2) \). Using the function \( g(x) = 3x + 5 \): \[ g(-2) = 3(-2) + 5 = -6 + 5 = -1 \] Now that we have \( g(-2) = -1 \), we can compute \( f(g(-2)) = f(-1) \). Using the function \( f(x) = 4 - x^{2} \): \[ f(-1) = 4 - (-1)^{2} = 4 - 1 = 3 \] Therefore, the value of \( f(g(-2)) \) is \( 3 \). In conclusion, the answer is \( \boxed{3} \).
