Question
Given that \( f(x)=5 x+1 \) and \( g(x)=1-x^{2} \), calculate (a) \( f(g(0))=\square \) (b) \( g(f(0))=\square \) Question Help: Dideo 1 Video 2 Submit Question
Ask by Olson Carlson. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) \( f(g(0)) = 6 \)
(b) \( g(f(0)) = 0 \)
Solution
### (a) Calculation of \( f(g(0)) \)
1. Compute \( g(0) \):
\[
g(0) = 1 - 0^2 = 1
\]
2. Substitute \( g(0) \) into \( f(x) \):
\[
f(1) = 5 \times 1 + 1 = 6
\]
Thus, \( f(g(0))= \boxed{6} \).
---
### (b) Calculation of \( g(f(0)) \)
1. Compute \( f(0) \):
\[
f(0) = 5 \times 0 + 1 = 1
\]
2. Substitute \( f(0) \) into \( g(x) \):
\[
g(1) = 1 - 1^2 = 0
\]
Thus, \( g(f(0))= \boxed{0} \).
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Simplify this solution Beyond the Answer
To solve the problem, let's break it down step by step. First, we need to find \( g(0) \): \[ g(0) = 1 - 0^2 = 1 - 0 = 1 \] Next, we substitute this result into \( f \): \[ f(g(0)) = f(1) = 5(1) + 1 = 5 + 1 = 6 \] So, \( f(g(0)) = 6 \). Now for part (b), we first find \( f(0) \): \[ f(0) = 5(0) + 1 = 0 + 1 = 1 \] Now, we substitute this result into \( g \): \[ g(f(0)) = g(1) = 1 - 1^2 = 1 - 1 = 0 \] Therefore, \( g(f(0)) = 0 \). Final answers: (a) \( f(g(0)) = 6 \) (b) \( g(f(0)) = 0 \)
