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\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]

Ask by Gardner Wright. in Ghana
Feb 18,2025

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(f ∘ g)(x) = 6x - 5

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Beyond the Answer

To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). Firstly, we calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now, using the definition of \( f(x) \): \[ f(x) = 3x + 4 \] we replace \( x \) with \( (2x - 3) \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Distributing the 3 gives: \[ = 6x - 9 + 4 \] Now, combine like terms: \[ = 6x - 5 \] Thus, the final answer is: \[ f \circ g(x) = 6x - 5 \]

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