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

Ask by Dunn Cox. in Nigeria
Feb 17,2025

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Answer

f ∘ g(x) = 6x - 5

Solution

To find f ∘ g(x), substitute g(x) into f(x): f(g(x)) = 3 * (2x - 3) + 4 = 6x - 9 + 4 = 6x - 5 Thus, f ∘ g(x) = 6x - 5.

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To find \( f \circ g(x) \), which means \( f(g(x)) \), we start by substituting \( g(x) \) into \( f(x) \). Given: - \( g(x) = 2x - 3 \) - \( f(x) = 3x + 4 \) Now substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify it: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, the composition \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]

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