Consider the following function: f: Z → N given by f(x) = (x+4)² +5; where, as usual, Z and N, denote the set of all integers and the set of all natural numbers, respectively. You are given that the function f is not an injection. In order to show that f is not an injection, state two distinct elements of the domain of f, denoted by ₁, 2, such that f(x₁) = f(x₂). ● State ₁: • State #₂: You are given that the function f is not a surjection. In order to show that f is not a surjection, state an element of the codomain of f, denoted by y, that is not in the image of f. • State y:

Consider the functions f : A → B, g : B → A and h : B → A such that if gf =14 and fh = 1B. Prove f is a 1-1 correspondence A - B. fla = f and 18f = f. (a) (b)

Find the domain of the function: f(x) O All Real Numbers O {x\ x=4} Ο Ο Ο O {x|x = 4, x= 3} O (X1X=3) 3} x2 - 5x+6 x² - 7x+12

The following functions all have domain {1, 2, 3, 4, 5} and codomain {1, 2, 3}. For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective nor surjective. a. f(n) = ( C. 1 2 3 4 5 1 Choose an answer: Select an answer b. f(n) = ( 1² (1²345) {² 2 3 1 2 2 Choose an answer: Select an answer x 3 Choose an answer: Select an answer î