(a) Let f(x) = r mod 3, where f(x) is the remainder when a is divided...

 

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(a) Let f(x) = r mod 3, where f(x) is the remainder when a is divided by 3, and f : N {0, 1, 2}. %3D i. Find f(7) and f(12). ii. What is the set of pre-images of 2. iii. Say whether or not f(a) is injective( one-to-one), justifying your an- [1] [1] swer. [2] iv. Say whether or not f(x) is surjective(onto), justifying your answer. [2] (b) Let B = {x : x € R and a # 1} and g : B→ B is defined by g(x) = . i. Show that the function g is a bijection. ii. Find g- [3] [2] (a) Let f(x) = r mod 3, where f(x) is the remainder when a is divided by 3, and f : N {0, 1, 2}. %3D i. Find f(7) and f(12). ii. What is the set of pre-images of 2. iii. Say whether or not f(a) is injective( one-to-one), justifying your an- [1] [1] swer. [2] iv. Say whether or not f(x) is surjective(onto), justifying your answer. [2] (b) Let B = {x : x € R and a # 1} and g : B→ B is defined by g(x) = . i. Show that the function g is a bijection. ii. Find g- [3] [2]