Let f : [-1,3] R be defined as f ( x ) = * 20 c | x | + [ x ], & … - Vidyadip

MCQ

Let $f : [-1,3] \to R$ be defined as

$f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{\left| x \right| + \left[ x \right],}&{ - 1 \leq x < 1} \\
{x + \left| x \right|,}&{1 \leq x < 2} \\
{x + \left| x \right|,}&{2 \leq x \leq 3}
\end{array}} \right.$

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

✓
only two points
B
only one point
C
four or more points
D
only three points

✓

Answer

Correct option: A.

only two points

a
$f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{ - x - 1}&{x \in \left[ { - 1,0} \right)}\\
x&{x \in \left[ {0,1} \right)}\\
{2x}&{x \in \left[ {1,2} \right)}\\
{x + 2}&{x \in \left[ {2,3} \right)}
\end{array}} \right.$

$f(x)$ is discontinuous at $x=0,1$

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