Prova Resolvida EFOMM(2024 - 2025) - Matemática - Questão 10

JapaMath Courses: Combo Mathematics for AFA/EsPCEx Officers + EFOMM Extension: https://pay.hotmart.com/I87122556D . Mathematics for AFA/EsPCEx Officers: https://pay.hotmart.com/T76099449M . EFOMM Extension: https://pay.hotmart.com/Q86479408Y . Hey guys! How are you? . In this video we will answer question 10 of the EFOMM 2024 - 2025 admission exam. . I hope you like it. . Happy studying! Follow me on social media: Instagram:   / japamath_   Facebook:   / wellington.nishio   Telegram: https://t.me/JapaMath Question 10 Regarding functions, analyze the alternatives below: I. The function tan(x), x ∈ [0,├ 𝜋/2)┤ is surjective in R+ and the function sen(x), with x ∈ R, is injective. II. The images of the families of functions f(x) = a|x| + b, with a and b ∈ R, do not contain negative numbers. III. The exponential function with base a, defined by f: R → 𝑅_+^∗, is denoted by f(x) = ax, where a is a positive real number different from 1. Suppose that the functions g(x) = b.ax and G(x) = B.Ax, with constants b, B ∈ 𝑅_+^∗, satisfy g(x1) = G(x1) and g(x2) = G(x2) for x1 ≠ x2. In this case, we have that a = A and b = B. IV. Quadratic and rational functions are defined on every real set. V. If the function f is non-injective and non-surjective and the function g is non-injective, then the composite function g or f is non-surjective. Select the correct option. (A) Only statements II, III, IV and V are true. (B) Only statements IV and V are true. (C) Only statement III is true. (D) Only statements I, II, and V are true. (E) Only statements I, III, and V are true.