JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \([ x ]\) be the greatest integer \(\leq x\). Then the number of points in the interval \((-2,1)\), where the function \(f(x)=|[x]|+\sqrt{x-[x]}\) is discontinuous is \(........\).
- A \(4\)
- B \(6\)
- C \(8\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
Need to check at doubtful points discont at \(x \in I\) only at \(x=-1 \Rightarrow f\left(-1^{+}\right)=1+0=1\) \(\Rightarrow f\left(-1^{-}\right)=2+1=3\) at \(x=0 \Rightarrow f\left(0^{+}\right)=0+0=0\) \(\Rightarrow f \left(0^{-}\right)=1+1=2\) at…
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