Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Pritchard Patel. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
To find the composition \( f \circ g(x) \), which is \( f(g(x)) \), follow these steps:
**Given Functions:**
\[
f(x) = 3x + 4
\]
\[
g(x) = 2x - 3
\]
**Step 1: Compute \( g(x) \)**
\[
g(x) = 2x - 3
\]
**Step 2: Substitute \( g(x) \) into \( f(x) \)**
\[
f(g(x)) = f(2x - 3)
\]
**Step 3: Apply the function \( f \) to \( g(x) \)**
\[
f(2x - 3) = 3(2x - 3) + 4
\]
**Step 4: Distribute and simplify**
\[
3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
\]
**Final Result:**
\[
f \circ g(x) = 6x - 5
\]
So, the composition \( f \circ g(x) \) is a linear function given by \( 6x - 5 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, we calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, we substitute \( g(x) \) into \( f(x) \): \[ f \circ g(x) = f(g(x)) = f(2x - 3) \] Next, we apply \( f(x) = 3x + 4 \) to \( 2x - 3 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify it: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, the result is: \[ f \circ g(x) = 6x - 5 \]
