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 - RB- Y -0- k -C- Y - N -0D- nY-k

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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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Similar questions

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

Q. A function

f : R \to R

is defined by

f (x + y) - k x y = f (x) + 2 y^{2} \forall x, y \in R

and

f (1) = 2; f (2) = 8

where k is some constant, then

f (x + y) . f (\frac{1}{x + y}) = (x + y \neq 0)

Q. Let

x + y = k

where

x, y > 0

and

S (k, n) = \sum_{r = 0}^{n} r^{2} ({^{n} C}_{r}) x^{r} y^{n - r}

then

Q. Assertion :Let f : R

\to

R be defined as

f (x) = a x^{2} + b x + c

, where a, b, c

ε

R and a

\neq

f (x) = 0

is having non-real roots, then

\int \frac{d x}{f (x)} = λ t a n^{- 1} (g (x)) + k

, where

λ

k

are constants and

g (x)

is linear function of

x

Reason:

t a n (t a n^{- 1} g (x)) = g (x) \forall x \in R

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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)=kGiven 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