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

Ask by Ortiz Dickson. in Mexico
Feb 22,2025

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f ∘ g(x) = 6x - 5

Solución

Para calcular la composición f ∘ g(x), seguimos estos pasos: 1. Dado que f(x) = 3x + 4 y g(x) = 2x - 3, sustituimos g(x) en f(x). Esto quiere decir que:   f ∘ g(x) = f(g(x)) = f(2x - 3). 2. Ahora, reescribimos f(2x - 3) utilizando la definición de f(x):   f(2x - 3) = 3(2x - 3) + 4. 3. Realizamos la multiplicación y la suma:   3(2x) = 6x, 3(-3) = -9, entonces:   6x - 9 + 4 = 6x - 5. La respuesta final es: f ∘ g(x) = 6x - 5.

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The Deep Dive

¡Claro! Para encontrar la composición de funciones \( f \circ g(x) \), primero necesitas sustituir \( g(x) \) en la función \( f(x) \). Dado que \( g(x) = 2x - 3 \), sustituimos esto en \( f(x) = 3x + 4 \): \[ f \circ g(x) = f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Ahora simplificamos: \[ = 6x - 9 + 4 = 6x - 5 \] Por lo tanto, \( f \circ g(x) = 6x - 5 \).

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