Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Rodriguez Stephens. in South Africa
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
Simplify the expression by following steps:
- step0: Add the terms:
\(3\left(2x-3\right)+4\)
- step1: Expand the expression:
\(6x-9+4\)
- step2: Add the numbers:
\(6x-5\)
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \).
1. Start with the functions:
- \( f(x) = 3x + 4 \)
- \( g(x) = 2x - 3 \)
2. Substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(2x - 3) = 3(2x - 3) + 4
\]
3. Now, expand the expression:
\[
3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
\]
Thus, the result is:
\[
f \circ g(x) = 6x - 5
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now, replace \( x \) in \( f(x) = 3x + 4 \) with \( 2x - 3 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Next, distribute the 3: \[ = 6x - 9 + 4 \] Combine like terms: \[ = 6x - 5 \] So, the result is: \[ f \circ g(x) = 6x - 5 \]
