Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Estrada Davey. in South Africa
Feb 21,2025
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Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
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Beyond the Answer
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 \( f(x) \): \[ f \circ g(x) = f(g(x)) = f(2x - 3) \] Now, replace \( x \) in \( f(x) = 3x + 4 \) with \( 2x - 3 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Next, distribute the 3: \[ = 6x - 9 + 4 \] Combine like terms: \[ = 6x - 5 \] Thus, the result is: \[ f \circ g(x) = 6x - 5 \]
