If f - R - R is defined by f x - sinn - x - - x- then the range of f x where - x - denotes integral part of x A- -1-1B- 0- -1-1-D- 1

The correct option is B { 0 }[x]=ϵ Z⇔ sin[x]π=tan[x]π=0 ; Where Z is an integer. ...

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Standard XII

Mathematics

Using Graph to Find Range of a Function

If f : R → R ...

Question

If $f : R \to R$ is defined by $f (x) = \frac{s i n [x] π + t a n [x] π}{1 + [x^{2}]}$ , then the range of f(x) (where [x] denotes integral part of x)

[- 1, 1]

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{- 1, 1}

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{1}

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{0}

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Solution

The correct option is D ${0}$
$[x] = ϵ Z \Leftrightarrow s i n [x] π = t a n [x] π = 0$ ; Where Z is an integer.

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Similar questions

Q. If

f : R \to R

is defined by

f (x) = \frac{s i n [x] π + t a n [x] π}{1 + [x^{2}]}

, then the range of f(x) (where [x] denotes integral part of x)

$i f f : R \to R i s d e f i n e d b y f (x) = \frac{s i n [x] π + t a n [x] π}{1 + [x^{2}]}, t h e n t h e r a n g e o f f = (w h e r e [x] d e n o t e s i n t e g r a l p a r t o f (x)$

Q. If

⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} [\frac{2 (sin x - {sin}^{n} x) + | sin x - {sin}^{n} x |}{2 (sin x - {sin}^{n} x) - | sin x - {sin}^{n} x |}], x \neq \frac{π}{2} 3, x = \frac{π}{2} \end{matrix}

where

[x]

denotes the integral part of

x

and

x \in (0, π)

and

n > 1

Show that

f (x)

is continuous and differentiable at

x = \frac{π}{2}

Q. If

f : R \to R

is defined by

f (x) = [\frac{x}{5}]

for

x \in R

, where

[y]

denotes the greatest integer not exceeding

y

, then

{f (x) : | x | < 71} =

Q. If

f (x) = \frac{sin ([x] π)}{x^{2} + x + 1}

, where

[x]

denotes the integral part of

x

. Show that

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is a constant function.

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If f:R→R is defined by f(x)=sin[x]π+tan[x]π1+[x2], then the range of f(x) (where [x] denotes integral part of x)

The correct option is D {0}[x]=ϵZ⇔sin[x]π=tan[x]π=0 ; Where Z is an integer.

If $f : R \to R$ is defined by $f (x) = \frac{s i n [x] π + t a n [x] π}{1 + [x^{2}]}$ , then the range of f(x) (where [x] denotes integral part of x)

The correct option is D ${0}$
$[x] = ϵ Z \Leftrightarrow s i n [x] π = t a n [x] π = 0$ ; Where Z is an integer.