In this assignment, N will denote the set of positive integers, Z the set of all integers, Q the set of all rational numbers, and R the set of all real numbers. After any problem statement, feel free to hit the Enter key as often as you need to make space for your answer.

Problem 1: Given A = {1, 2, 3, 4, 5} and B = {a, b, c, d, e}, which of the following functions  from A to B are one-to-one, onto, neither one-to-one nor onto, or both one-to-one and onto?

(a)     {(1,b), (2,c), (3,a), (4,d), (5,e)}

(b)   {(1,d), (2,a), (3,c), (4,a), (5,b)}

Problem 2: Which of the following functions from R to R are one-to-one, onto, neither one-to-one nor onto, or both one-to-one and onto?

(a)

(b)

(c)

Problem 3: Let f: N à N be defined by f(n) = 6n - 5. Does f ^-1 exist? If so, find it.  If not, explain why not.

Problem 4: Find the inverse of the function f(x) = -7x + 13 from R to R.

Problem 5: Let f and g be functions from R to R defined by f(x) = 3x + 1 and g(x) = x³.

(a) Find

(b) Find

Problem 6: Find the images of each of the following functions from R to R.

(a)

(b)

(c)

Problem 7: Find the image of the following function from R to R.

f(x) = x⁴ - 4x³ + 6x² - 4x + 2