Para resolver a questão, precisamos calcular as composições das funções \( f \) e \( g \). 1. Cálculo de \( (f \circ g)(x) \): - \( g(x) = \operatorname{sen} x \) - Então, \( (f \circ g)(x) = f(g(x)) = f(\operatorname{sen} x) = 1 - 2(\operatorname{sen} x) = 1 - 2 \operatorname{sen} x \). 2. Cálculo de \( (g \circ f)(x) \): - \( f(x) = 1 - 2x \) - Então, \( (g \circ f)(x) = g(f(x)) = g(1 - 2x) = \operatorname{sen}(1 - 2x) \). Agora, temos: - \( (f \circ g)(x) = 1 - 2 \operatorname{sen} x \) - \( (g \circ f)(x) = \operatorname{sen}(1 - 2x) \) Analisando as alternativas: a. \( (f \circ g)(x)=1+2 \operatorname{sen} x \) e \( (g \circ f)(x)=\operatorname{sen}(-2 x) \) - Incorreto. b. \( (f \circ g)(x)=-2 \operatorname{sen} x \) e \( (g \circ f)(x)=\operatorname{sen}(1-2 x) \) - Incorreto. c. \( (f \circ g)(x)=1-2 \operatorname{sen} x \) e \( (g \circ f)(x)=\operatorname{sen}(1-2 x) \) - Correto. d. \( (f \circ g)(x)=1-2 \operatorname{sen} x \) e \( (g \circ f)(x)=\operatorname{sen} x .(1-2 x) \) - Incorreto. e. \( (f \circ g)(x)=1+2 \operatorname{sen} x \) e \( (g \circ f)(x)=\operatorname{sen} x .(1-2 x) \) - Incorreto. Portanto, a alternativa correta é: c. \( (f \circ g)(x)=1-2 \operatorname{sen} x \) e \( (g \circ f)(x)=\operatorname{sen}(1-2 x) \).