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Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, g, circle, f, right parenthesis, left parenthesis, 0, right parenthesis, .(g∘f)(0).f, of, x, equals, 2, x, squared, plus, 2, x, minus, 3f(x)=2x 2 +2x−3g, of, x, equals, minus, 5, x, plus, 3g(x)=−5x+3

Question

Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, g, circle, f, right parenthesis, left parenthesis, 0, right parenthesis, .(g∘f)(0).f, of, x, equals, 2, x, squared, plus, 2, x, minus, 3f(x)=2x 2 +2x−3g, of, x, equals, minus, 5, x, plus, 3g(x)=−5x+3

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Solution

Para resolver el problema, debemos encontrar el valor de (g∘f)(0)(g \circ f)(0). Esto significa que primero debemos evaluar f(0)f(0) y luego usar ese resultado para evaluar gg.

Dado: f(x)=2x2+2x−3 f(x) = 2x^2 + 2x - 3 g(x)=−5x+3 g(x) = -5x + 3

Primero, evaluamos f(0)f(0): f(0)=2(0)2+2(0)−3 f(0) = 2(0)^2 + 2(0) - 3 f(0)=−3 f(0) = -3

Ahora, usamos este resultado para evaluar g(f(0))g(f(0)), es decir, g(−3)g(-3): g(−3)=−5(−3)+3 g(-3) = -5(-3) + 3 g(−3)=15+3 g(-3) = 15 + 3 g(−3)=18 g(-3) = 18

Por lo tanto, el valor de (g∘f)(0)(g \circ f)(0) es: (g∘f)(0)=18 (g \circ f)(0) = 18

This problem has been solved

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