Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Floyd Watkins. in Nigeria
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. **Write the composite function \( f \circ g(x) \):**
\[
f \circ g(x) = f(g(x))
\]
2. **Substitute \( g(x) \) into \( f(x) \):**
Given \( g(x) = 2x - 3 \), we have
\[
f(g(x)) = f(2x - 3)
\]
3. **Apply \( f(x) = 3x + 4 \) with \( x = 2x - 3 \):**
\[
f(2x - 3) = 3(2x - 3) + 4
\]
4. **Simplify the expression:**
\[
3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
\]
5. **Final Answer:**
\[
f \circ g(x) = 6x - 5
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, we compute \( g(x) \): \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now plug in \( 2x - 3 \) into \( f(x) \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Distributing inside the parentheses: \[ = 6x - 9 + 4 \] Combine like terms: \[ = 6x - 5 \] Thus, \( f \circ g(x) = 6x - 5 \).
