Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Maxwell Schwartz. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. We need to compute the composition \( f \circ g(x) = f(g(x)) \).
2. Given that \( g(x) = 2x - 3 \), substitute it into \( f(x) \):
\[
f(g(x)) = f(2x-3)
\]
3. The definition of \( f(x) \) is \( f(x) = 3x + 4 \), so replacing \( x \) with \( 2x - 3 \) yields:
\[
f(2x-3) = 3(2x-3) + 4
\]
4. Distribute the \( 3 \) inside the parentheses:
\[
3(2x-3) = 6x - 9
\]
5. Add \( 4 \) to the result:
\[
6x - 9 + 4 = 6x - 5
\]
6. Therefore, the composition is:
\[
f \circ g(x) = 6x - 5
\]
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Simplify this solution Beyond the Answer
To find \( (f \circ g)(x) \), we need to substitute \( g(x) \) into \( f(x) \). We start with \( g(x) = 2x - 3 \). Now, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify it: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Therefore, \[ (f \circ g)(x) = 6x - 5. \]
