2. recall from lecture 3-1 the definition of the restriction of a function f : a + b to a subset c ca, denoted flc. (a) let f: z r be defined by f(n) = sin " find a subset c cz with as many elements as possible, such that flc is injective. (b) let f.9: a + b be two functions. suppose that c and d are subsets of a which are not equal to a, such that flc = glc and fp = g|d. give an example of such sets a, b, c, d and functions f and g such that f and g are not equal. find a condition on c and d that guarantees that f = 9, and prove that your condition works. (try not to make your condition more restrictive than necessary! ) (c) now suppose that c, d are subsets of a, and that f: c → b and g: d → b are functions. what condition on f and g is necessary to ensure that there exists a function h: a + b such that hlc = f and h|d = g?