Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Wilson Mccarthy. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
To find the composition \( f \circ g(x) \), we need to evaluate \( f(g(x)) \). Here's how you can do it step by step:
**Given:**
\[
f(x) = 3x + 4
\]
\[
g(x) = 2x - 3
\]
**Step 1:** Find \( g(x) \)
\[
g(x) = 2x - 3
\]
**Step 2:** Substitute \( g(x) \) into \( f(x) \)
\[
f(g(x)) = f(2x - 3) = 3(2x - 3) + 4
\]
**Step 3:** Simplify the expression
\[
f(g(x)) = 3(2x) - 3(3) + 4 = 6x - 9 + 4 = 6x - 5
\]
**Final Answer:**
\[
f \circ g(x) = 6x - 5
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find \( f \circ g(x) \), we need to calculate \( f(g(x)) \). First, substitute \( g(x) \) into \( f(x) \): \[ g(x) = 2x - 3 \] Now, substitute this into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now, distribute and simplify: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Therefore, \[ f \circ g(x) = 6x - 5 \]
