# 1. Consider the function h:Z+ +Z+ defined by h(n) = l{k e Z+ : k|n}l. The...

###### Question:

1. Consider the function h:Z+ +Z+ defined by h(n) = l{k e Z+ : k|n}l. The bars around the set mean that we are taking the size of the set. Thus h(n) is the number of positive divisors of n. (a) Make a table of values for h(n) for 1 sn < 10. Write one or two sentences describing how you found the values in the table. (b) Find the value of h(90). Explain how you found your answer. (c) Find the value of h(2). The answer will be a simple formula involving m. (d) Is h a one-to-one function? Why or why not? (e) Is h an onto function? Why or why not? (f) Describe the set h+(2). Explain your reasoning.

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