Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Cummings Nguyen. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. Substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = 3 \cdot g(x) + 4
\]
2. Replace \( g(x) \) with \( 2x-3 \):
\[
f(g(x)) = 3(2x-3) + 4
\]
3. Distribute \( 3 \):
\[
f(g(x)) = 6x - 9 + 4
\]
4. Combine like terms:
\[
f(g(x)) = 6x - 5
\]
Thus, the composition \( f \circ g(x) \) is \( 6x-5 \).
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Simplify this solution The Deep Dive
To find \( f \circ g(x) \), you need to substitute \( g(x) \) into \( f(x) \). First, calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now simplify it: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] So, the answer is: \[ f \circ g(x) = 6x - 5 \]
