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 k - N- If Y is the range of f x - thenA- Y-N -0B- nY-kC- Y -0- k -D- Y - R

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Define x % a ...

Question

Define $x % a$ as the remainder obtained when $x$ is divided by $a$ .
Let $f : Z \to R$ be defined as $f (x) = x % k$ , where $k ϵ N$ . If Y is the range of $f (x)$ , then

$Y = R$

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$Y = [0, k]$

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$Y = N \cup {0}$

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$n (Y) = k$

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Solution

The correct option is D
$n (Y) = k$

Given x is an integer and k is a natural number, x can be expressed as
$x = q . k + r$ , where $q, r ϵ Z$ and $0 \leq r < k$ .
i.e. the remainder can be any value from 0 to k-1
$\Rightarrow r ϵ {0, 1, 2 . . . . . . . k - 1} \Rightarrow f (x) ϵ {0, 1, 2 . . . . . . . . k - 1} \Rightarrow Y = {0, 1, 2, . . . . . . . . . . k - 1} \Rightarrow n (Y) = k$

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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 k ϵ N. If Y is the range of f(x), then

The correct option is D n(Y)=k Given x is an integer and k is a natural number, x can be expressed as x=q.k+r, where q,r ϵ Z and 0≤r<k. i.e. the remainder can be any value from 0 to k-1 ⇒r ϵ {0,1,2.......k−1}⇒f(x) ϵ {0,1,2........k−1}⇒Y={0,1,2,..........k−1}⇒n(Y)=k

Define $x % a$ as the remainder obtained when $x$ is divided by $a$ .
Let $f : Z \to R$ be defined as $f (x) = x % k$ , where $k ϵ N$ . If Y is the range of $f (x)$ , then