Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Cox Bird. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
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Mind Expander
To find the composition \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, we calculate \( g(x) \): \[ g(x) = 2x - 3. \] Next, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3). \] Now, recall that \( f(x) = 3x + 4 \). So, substituting \( 2x - 3 \) into \( f \): \[ f(2x - 3) = 3(2x - 3) + 4. \] Now simplify: \[ = 6x - 9 + 4, \] \[ = 6x - 5. \] Therefore, the composition \( f \circ g(x) = 6x - 5 \).
