Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Tucker Donnelly. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. We substitute \( g(x) \) into \( f(x) \) to form the composite function:
\[
f(g(x)) = f(2x-3)
\]
2. Replace \( x \) in \( f(x) = 3x+4 \) with \( 2x-3 \):
\[
f(2x-3) = 3(2x-3) + 4
\]
3. Distribute the \( 3 \):
\[
3(2x-3) = 6x - 9
\]
4. Add \( 4 \) to the expression:
\[
6x - 9 + 4 = 6x - 5
\]
Thus, the composite function is:
\[
f \circ g(x) = 6x - 5
\]
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Simplify this solution Bonus Knowledge
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'll substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Next, we apply the function \( f(x) \): \[ f(x) = 3x + 4 \] So, \[ f(2x - 3) = 3(2x - 3) + 4 \] Now we distribute: \[ = 6x - 9 + 4 \] Combining like terms gives us: \[ = 6x - 5 \] Thus, \[ f \circ g(x) = 6x - 5 \]
