Please answer the question in its entirety. 2. Consider the function ƒ: R → [−1, 1] defined by ƒ(x) = sin(x) and the function g: [-π/2, π/2] → [−1, 1] defined by g(x) = sin(x).A. The function f is not injective, and the function g is injective. Explain.B. The inverse function of g will have a domain of [−1, 1] and a range of [-π/2, π/2]. Explain. (Henceforth, we will refer to the inverse function to g asy = sin¯¹(x).)C. For any x on the interval [−1, 1], the value of cos(sin¯¹ (x)) will be nonnegative. Explain.D. Utilizing the identity sin² (y) + cos² (y) = 1 and your result from Part C above, deduce that cos(sin−¹(x)) is equal to √1 – x² (and not-√1-x²).

A. The function f(x) = sin(x) on the domain [-1, 1] is not injective because it takes on the same…

2. Consider the function f: R → [-1, 1] defined by f(x) = sin(x) and the function g: [-π/2, π/2] → [-1, 1] defined by g(x) = sin(x). A. The function f is not injective, and the function g is injective. Explain. B. The inverse function of g will have a domain of [-1, 1] and a range of [-T/2, π/2]. Explain. (Henceforth, we will refer to the inverse function to g as y = sin ¹(x).) C. For any on the interval [-1, 1], the value of cos (sin-¹(x)) will be nonnegative. Explain. D. Utilizing the identity sin² (y) + cos² (y) = 1 and your result from Part C above, deduce that cos(sin-¹(x)) is equal to √1-x²). - x² (and not

2. Consider the function f: R → [-1, 1] defined by f(x) = sin(x) and the function g: [-π/2, π/2] → [-1, 1] defined by g(x) = sin(x). A. The function f is not injective, and the function g is injective. Explain. B. The inverse function of g will have a domain of [-1, 1] and a range of [-T/2, π/2]. Explain. (Henceforth, we will refer to the inverse function to g as y = sin ¹(x).) C. For any on the interval [-1, 1], the value of cos (sin-¹(x)) will be nonnegative. Explain. D. Utilizing the identity sin² (y) + cos² (y) = 1 and your result from Part C above, deduce that cos(sin-¹(x)) is equal to √1-x²). - x² (and not

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 55E

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