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

Ask by Santiago Sandoval. in Argentina
Feb 22,2025

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f ∘ g(x) = 6x - 5

Solución

Para encontrar la composición f ∘ g(x), primero sustituimos g(x) en f(x): f(g(x)) = 3(g(x)) + 4 Sustituye g(x) = 2x - 3: f(g(x)) = 3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5.

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The Deep Dive

¡Claro! Para encontrar \( f \circ g(x) \), primero debemos sustituir \( g(x) \) dentro de \( f(x) \). 1. Calculamos \( g(x) \): \[ g(x) = 2x - 3 \] 2. Ahora sustituimos \( g(x) \) en \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] \[ = 6x - 9 + 4 = 6x - 5 \] Por lo tanto, \( f \circ g(x) = 6x - 5 \).

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