Define x%a as the remainder obtained when x is divided by a. Let f:Z→R be defined as f(x)=x%k, where kϵN. If Y is the range of f(x), then
A
Y=R
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B
Y=[0,k]
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C
Y=N∪{0}
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D
n(Y)=k
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Solution
The correct option is Dn(Y)=k Given x is an integer and k is a natural number, x can be expressed as x=q.k+r, where q,rϵZ and 0≤r<k. i.e. the remainder can be any value from 0 to k-1 ⇒rϵ{0,1,2.......k−1}⇒f(x)ϵ{0,1,2........k−1}⇒Y={0,1,2,..........k−1}⇒n(Y)=k