Question

Find the domain and range of this functions

a) The function that assigns to each pair of positive integer the maximum of these two integers

b) The function that assigns to each positive integer the number of the digits 0,1,2,3,4,5,6,7,8,9 that do not appear as decimal digits of the integer.

Answer 1

Let $\N$ denotes the set of positive integers.

a) It follows that $dom(f)=\N\times\N,$ and $range(f)=\N.$

b) Since each integer number contains at least one digit, and hence $10\notin range(f),$ we conclude that $dom(f)=\N,$ and $range(f)=\{0,1,2,3,4,5,6,7,8,9\}.$