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1. Suppose f : A - A such that f of is bijective. Is f necessarily bijective? 2. Suppose that f : A - B is a surjectiveand Y C B. Show that f ( f - 1 ( Y ) ) = Y. 3. Let f : E - F be a function. We recall that for any A C E, the image f(A) of A by f is defined as f( A) = {f(x) : " EA }. Show that f is surjective if and only if (\\a)is()f\\ '(@)daVA 4. (a) Prove that the function g : R2 -> R, g(x, y) = x2 - y2, is surjective. (b) Find g-'({0}). (c) Let A := {a E R : a 2 0} and consider the function h : A -> A, h(x) = x +3. Find h-'({c} ) for each c in the codomain