1. Define f : → by f (x) = x2. Find f–1 (T ) for each of the following. (a) T = {9} (b) T = [4, 9) (c) T = [– 4, 9 2. Suppose f : A → B and S and T are subsets of A. Prove or give a counterexample....

1. Define f :

→

by f (x) = x². Find f^–1
(T ) for each of the following.

(a) T = {9}

(b) T = [4, 9)

(c) T = [– 4, 9

2. Suppose f : A → B and S and T are subsets of A. Prove or give a counterexample.

(a) If S ⊆ T, then f (S ) ⊆ f (T ).

(b) If f (S ) ⊆ f (T ), then S ⊆ T