Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Pearson Greene. in Nigeria
Feb 03,2025
Real Tutor 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. We have the functions:
- \( f(x) = 3x + 4 \)
- \( g(x) = 2x - 3 \)
2. Now, we substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(2x - 3)
\]
3. Next, we calculate \( f(2x - 3) \):
\[
f(2x - 3) = 3(2x - 3) + 4
\]
4. Expanding this expression:
\[
= 6x - 9 + 4
\]
\[
= 6x - 5
\]
Thus, the result is:
\[
f \circ g(x) = 6x - 5
\]
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Simplify this solution The Deep Dive
To find \( f \circ g(x) \), which means \( f(g(x)) \), we'll first substitute \( g(x) \) into \( f(x) \). Given: \[ g(x) = 2x - 3 \] Now substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now simplify: \[ = 6x - 9 + 4 \] Combine like terms: \[ = 6x - 5 \] Thus, the final result is: \[ f \circ g(x) = 6x - 5 \]
