PRACTICE EXERCISES

1. Let A = {1, 2, 3, 4, 5} and B = {a, b, c, d}. Which of the following arrow diagram(s) defines onto functions? Explain.

2. Define functions f from Z to Z and g from R to R by the formulas: for all yZ and xR,

    f(y) =  y²    and g(x) = 2x + 1

   a. Is f onto? Prove or disprove by giving a counter example.

   b. Is g onto? Prove or disprove by giving a counter example.