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

Ask by Whittaker Hampton. in Ghana
Feb 21,2025

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f ∘ g(x) = 6x - 5

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Beyond the Answer

To find \( f \circ g(x) \), also known as the composition of functions, we substitute \( g(x) \) into \( f(x) \). First, calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f \circ g(x) = f(g(x)) = f(2x - 3) \] Next, use the formula for \( f(x) \): \[ f(x) = 3x + 4 \] So now we replace \( x \) in \( f(x) \) with \( 2x - 3 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, the final answer is: \[ f \circ g(x) = 6x - 5 \]

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