Question
Using the following equations, find \( f(g(x)) \) : \( f(x)=x+8 \) \( g(x)=x^{4} \) \( f(g(x))=x^{[?]}+\square \)
Ask by Clarke Nguyen. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(g(x)) = x^{4} + 8 \)
Solution
To find \( f(g(x)) \), we'll substitute \( g(x) \) into \( f(x) \).
Given:
- \( f(x) = x + 8 \)
- \( g(x) = x^4 \)
**Step-by-Step Solution:**
1. **Substitute \( g(x) \) into \( f(x) \):**
\[
f(g(x)) = f(x^4)
\]
2. **Apply the function \( f \) to \( x^4 \):**
\[
f(x^4) = x^4 + 8
\]
**Final Expression:**
\[
f(g(x)) = x^4 + 8
\]
So, filling in the blanks:
\[
f(g(x)) = x^{4} + 8
\]
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
To find \( f(g(x)) \), we start by substituting \( g(x) = x^4 \) into the function \( f(x) \). First, we can rewrite \( f(g(x)) \) as: \[ f(g(x)) = f(x^4) \] Now, applying the function \( f(x) = x + 8 \): \[ f(x^4) = x^4 + 8 \] Therefore, we can express \( f(g(x)) \) as: \[ f(g(x)) = x^{4} + 8 \] So \( f(g(x)) = x^{[4]} + \square \) where \( \square = 8 \).
