Just need help on a and b 12. Let Rs = {0, 1, 2, 3, 4}.(a) Define f: R5 R5 by f(x) = x² + 4 (mod 5) for all x e R5. Writethe inverse of f as a set of ordered pairs and explain why fis not afunction.(b) Define g: R5 → R5 by g(x) = x³ + 4 (mod 5) for all x e R5. Writethe inverse of g as a set of ordered pairs and explain why g-1is afunction.(c) Is it possible to write a formula for g(y), where y e R5? The answerto this question depends on whether or not is possible to define a cuberoot of elements of R5. Recall that for a real number x, we define thecube root of x to the real number y such that y3 = x. That is,y = Yx if and only if y3 = x.Using this idea, is it possible to define the cube root of each number inZs? If so, what are 0, Vī, 2, V3, and 4.(d) Now answer the question posed at the beginning of Part (c). If possible,determine a formula for g(y) where g-1: R5 → R5.Explorations and Activities

Name: Just need help on a and b 12. Let Rs = {0, 1, 2, 3, 4}.(a) Define f: R
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Just need help on a and b 12. Let Rs = {0, 1, 2, 3, 4}.(a) Define f: R5 R5 by f(x) = x² + 4 (mod 5) for all x e R5. Writethe inverse of f as a set of ordered pairs and explain why fis not afunction.(b) Define g: R5 → R5 by g(x) = x³ + 4 (mod 5) for a