Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Stuart Rowe. in Norway
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
```markdown
# Composition of Functions: \( f \circ g(x) \)
Given the functions:
\[
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3
\]
To find the composition \( f \circ g(x) \), we compute \( f(g(x)) \):
\[
f(g(x)) = f(2x - 3) = 3(2x - 3) + 4
\]
Simplifying the expression:
\[
f(g(x)) = 6x - 9 + 4 = 6x - 5
\]
**Therefore, the composition is:**
\[
f \circ g(x) = 6x - 5
\]
```
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Simplify this solution Mind Expander
To find \( f \circ g(x) \), which means \( f(g(x)) \), we first need to substitute \( g(x) \) into \( f(x) \). 1. We have \( g(x) = 2x - 3 \). 2. Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] 3. The function \( f(x) = 3x + 4 \). Replace \( x \) in \( f(x) \) with \( 2x - 3 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] 4. Now, distribute \( 3 \): \[ = 6x - 9 + 4 \] 5. Combine like terms: \[ = 6x - 5 \] So, \( f \circ g(x) = 6x - 5 \).
