1. Determine whether each of these functions from

{a, b, c, d} to itself is one-to-one.

a) f (a) = b, f (b) = a, f (c) = c, f (d) = d

b) f (a) = b, f (b) = b, f (c) = d, f (d) = c

c) f (a) = d, f (b) = b, f (c) = c, f (d) = d

2. Which functions in Exercise 1 are onto?

3. Determine whether each of these functions from Z to Z is one-to-one.

a) f (n) = n − 1 

b) f (n) = n^2 + 1

c) f (n) = n^3

d) f (n) = [n/2]

4. Determine whether each of these functions is a bijection from R to R.

a) f (x) = 2x + 1

b) f (x) = x^2 + 1

c) f (x) = x^3

d) f (x) = (x^2 + 1)/(x^2 + 2)