Question
Suppose \( f(x)=1-x^{2} \) and \( g(x)=2 x+5 \) Find the value of \( f(g(-1)) \).
Ask by Guzman Whittaker. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(g(-1)) = -8 \)
Solution
To find \( f(g(-1)) \), follow these steps:
1. **Evaluate \( g(-1) \):**
\[
g(x) = 2x + 5
\]
Plugging in \( x = -1 \):
\[
g(-1) = 2(-1) + 5 = -2 + 5 = 3
\]
2. **Now, evaluate \( f(g(-1)) = f(3) \):**
\[
f(x) = 1 - x^2
\]
Plugging in \( x = 3 \):
\[
f(3) = 1 - (3)^2 = 1 - 9 = -8
\]
**Final Answer:** \(-8\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find \( f(g(-1)) \), we first need to evaluate \( g(-1) \). Starting with the function \( g(x) = 2x + 5 \): \[ g(-1) = 2(-1) + 5 = -2 + 5 = 3 \] Now that we have \( g(-1) = 3 \), we can find \( f(g(-1)) = f(3) \) using the function \( f(x) = 1 - x^{2} \): \[ f(3) = 1 - (3)^{2} = 1 - 9 = -8 \] Thus, the value of \( f(g(-1)) \) is \(-8\).
