JEE Mains · Maths · STD 12 - 5. continuity and differentiation
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:
- A only two points
- B only one point
- C four or more points
- D only three points
Answer & Solution
Correct Answer
(A) only two points
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} { - x - 1}&{x \in \left[ { - 1,0} \right)}\\ x&{x \in \left[ {0,1} \right)}\\ {2x}&{x \in \left[ {1,2} \right)}\\ {x + 2}&{x \in \left[ {2,3} \right)} \end{array}} \right.\) \(f(x)\) is discontinuous at \(x=0,1\)
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