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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.
There is a staircase as shown in figure connecting points A and B. Measurements of steps are marked in the figure. Find the straight distance between A and B. (Ans:10) A ns
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