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

Ask by Malone Ingram. in South Africa
Feb 22,2025

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f ∘ g(x) = 6x − 5

Solución

We are given the functions:   f(x) = 3x + 4   g(x) = 2x − 3 To find the composition f ∘ g(x), substitute g(x) into f(x):   f(g(x)) = 3(2x − 3) + 4 Now, simplify the expression:   = 6x − 9 + 4   = 6x − 5 Thus, f ∘ g(x) = 6x − 5.

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Mind Expander

To find \( f \circ g(x) \), which is the composition of the functions \( f \) and \( g \), we need to substitute \( g(x) \) into \( f(x) \). 1. Start by finding \( g(x) \): \[ g(x) = 2x - 3 \] 2. Now substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] 3. Simplify the expression: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, \( f \circ g(x) = 6x - 5 \).

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