Let A and B be two sets each with finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.

Fill in the blanks in each of the

Let f :R → R be defined by. Then (f o f o f) (x) = _______

Let f : [2, ∞) → R be the function defined by f (x) = x²–4x+5, then the range of f is

Let f : N → R be the function defined byand g : Q → R be another function defined by g (x) = x + 2. Then (g o f)3/2 is

Fill in the blanks in each of the

Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = ______and f o g = ______.

Let f :R → R be defined by

Then f (– 1) + f (2) + f (4) is

Let f : [0, 1] → [0, 1] be defined by

Then (f o f) x is

Which of the following functions from Z into Z are bijections?