Exercise 2.11. Prove that n = for all n E Z. Exercise 212 Determnine whether or not the given functions

Let g be the successor function defined from Z to Z by the formula g(n) = n + 1. g(-3,000) = g(0) = g(2,999)

EXERCISE 2.12.2: Composition of functions on integers. Consider three functions f, g, and h, whose domain and target are Z. Let f(x)=x2           g(x)=2x           h(x)=⌈x5⌉   (b) Evaluate (f ο h)(52) (c) Evaluate (g ο h ο f)(4)

Consider the function f: {1, 2, 3, 4} → {1, 2, 3, 4} given by f(n) = a. Find f(1) b. Find an element n in the domain such that f(n) = 1 c. Find an element n in the domain such that f(n) = n 2 3 = (2 ²44) d. Find an element of the codomain that is not in the range.