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

Ask by Bolton Martinez. in Ghana
Feb 11,2025

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(f ∘ g)(x) = 6x - 5

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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 will substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now, substitute \( 2x - 3 \) into \( f(x) = 3x + 4 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Distributing the \( 3 \): \[ = 6x - 9 + 4 \] Combining like terms: \[ = 6x - 5 \] Therefore, \( f \circ g(x) = 6x - 5 \).

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