Determine the range of given algorithm, Mathematics

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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.

(a) What is the range of f? Based on your answer, is f onto?

(b) Determine whether f a 1-1 function.

 


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