Let f - -1- 3- - R be defined as f - -x- - -x- - -1- x - 1 x-x- - 1 - x - 2 x - -x- - 2 - x - 3- where -t- denotes the greatest integer less than or equal to t- then- f is discontinuous at-

The correct option is C only three points f(x) = #160; (x+ 1) amp;, amp; 1≤ x ≤ 0 x amp; , #10; amp; 0 ≤ x lt; 1 #160; 2x ...

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Byju's Answer

Standard XII

Mathematics

Absolute Value Function

Let f : [-1...

Question

Let $f : [- 1, 3] \to R$ be defined as
$f = ⎧ ⎨ ⎩ \begin{matrix} | x | + [x] & , & - 1 \leq x < 1 x + | x | & , & 1 \leq x < 2 x + [x] & , & 2 \leq x \leq 3 \end{matrix}$ ,
where [t] denotes the greatest integer less than or equal to $t$ . then, $f$ is discontinuous at:

four or more points

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only one point

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only two points

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only three points

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Solution

The correct option is C only three points
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - (x + 1) & , & - 1 \leq x \leq 0 x & , & 0 \leq x < 1 2 x & , & 1 \leq x < 2 x + 2 & , & 2 \leq x < 3 x + 3 & , & x = 3 \end{matrix}$
function discontinuous at $x = 0, 1, 3$

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Similar questions

Q. Let

f : [- 1, 3] \to R

be defined as

f (x) = ⎧ ⎨ ⎩ \begin{matrix} | x | + [x], - 1 \leq x < 1 x + | x |, 1 \leq x < 2 x + [x], 2 \leq x \leq 3 \end{matrix}

where

[t]

denotes the greatest integer less than or equal to

t

. Then,

f

is discontinuous at :

Q. Let

f : [- 1, 3] \to R

be defined as

f (x) = ⎧ ⎨ ⎩ \begin{matrix} | x | + [x], - 1 \leq x < 1 x + | x |, 1 \leq x < 2 x + [x], 2 \leq x \leq 3 \end{matrix}

where

[t]

denotes the greatest integer less than or equal to

t

. Then,

f

is discontinuous at :

Q. Let

f (x) = [2 x^{3} - 6]

when

[x]

is greatest integer less than or equal to

x

then the number of points in (1,2) where

f

is discontinuous is

Q. For a real number

x

, let

[x]

denote the greatest integer less than or equal to

x

. Let

f : R \to R

be defined as

f (x) = 2 x + [x] + sin x . cos x

then

f

Q. Let

f : (0, \infty) \to [1, \infty)

be defined as

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1}{x}, & 0 < x < 1 \frac{x}{[x]}, & 1 \leq x < \infty \end{matrix}

where

[x]

denotes the greatest integer less than or equal to

x .

Then which of the following statements is (are) CORRECT?

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Let f:[−1,3]→R be defined asf=⎧⎨⎩|x|+[x],−1≤x<1x+|x|,1≤x<2x+[x],2≤x≤3, where [t] denotes the greatest integer less than or equal to t. then, f is discontinuous at:

The correct option is C only three pointsf(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪⎩−(x+1),−1≤x≤0x,0≤x<12x,1≤x<2x+2,2≤x<3x+3,x=3function discontinuous at x=0,1,3

Let $f : [- 1, 3] \to R$ be defined as
$f = ⎧ ⎨ ⎩ \begin{matrix} | x | + [x] & , & - 1 \leq x < 1 x + | x | & , & 1 \leq x < 2 x + [x] & , & 2 \leq x \leq 3 \end{matrix}$ ,
where [t] denotes the greatest integer less than or equal to $t$ . then, $f$ is discontinuous at:

The correct option is C only three points
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - (x + 1) & , & - 1 \leq x \leq 0 x & , & 0 \leq x < 1 2 x & , & 1 \leq x < 2 x + 2 & , & 2 \leq x < 3 x + 3 & , & x = 3 \end{matrix}$
function discontinuous at $x = 0, 1, 3$