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)