Question
Let \( f(x)=x^{2}-3 \) and \( g(x)=\sqrt{x+7} \). Find \( f(g(2)) \) O 6 O \( 2 \sqrt{2} \)
Ask by Campbell Love. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(g(2)) = 6 \)
Solution
To find \( f(g(2)) \), we'll follow these steps:
1. **Calculate \( g(2) \):**
\[
g(x) = \sqrt{x + 7}
\]
\[
g(2) = \sqrt{2 + 7} = \sqrt{9} = 3
\]
2. **Now, compute \( f(g(2)) = f(3) \):**
\[
f(x) = x^2 - 3
\]
\[
f(3) = 3^2 - 3 = 9 - 3 = 6
\]
So, \( f(g(2)) = 6 \).
**Answer:** 6
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find \( f(g(2)) \), we first need to evaluate \( g(2) \). Starting with the function \( g(x) = \sqrt{x + 7} \): \[ g(2) = \sqrt{2 + 7} = \sqrt{9} = 3. \] Now, we substitute this value into the function \( f(x) = x^2 - 3 \): \[ f(g(2)) = f(3) = 3^2 - 3 = 9 - 3 = 6. \] Thus, the result is \( \boxed{6} \).
