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# Help me answer: - Limit , continuity and differentiability - JEE Main-16

Let $f:\left [ -1,3 \right ]\rightarrow R$ be defined as

$f(x)=\left\{\begin{matrix} \left | x \right |+\left [ x \right ],\: \: \: \: \: \: &-1\leq x<1 \\ x+\left | x \right |, &\: 1\leq x<2 \\ x+\left [ x \right ], &\: \: 2\leq x\leq 3, \end{matrix}\right.$

where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at :

• Option 1)

only one point

• Option 2)

only two points

• Option 3)

only three points

• Option 4)

four or more points

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$f(x)=\left\{\begin{matrix} \left | x \right |+\left [ x \right ],\: \: \: \: \: \: &-1\leq x<1 \\ x+\left | x \right |, &\: 1\leq x<2 \\ x+\left [ x \right ], &\: \: 2\leq x\leq 3, \end{matrix}\right.$

$f(x)=\left\{\begin{matrix} -x-1, &-1\leq x<0 \\ x+0,&0\leq x<1 \\ 2x, &1\leq x<2 \\ x+2, & 2\leq x<3\\ x+3, & x=3 \end{matrix}\right.$

$f(x)$ is discontinuous at $x=0,1,3.$

Option 1)

only one point

Option 2)

only two points

Option 3)

only three points

Option 4)

four or more points

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