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Let [x] be the greatest integer\leq x. Then the number of points in the interval (-2,1), where the function \mathrm{f}(\mathrm{x})=[[\mathrm{x}] \mid+\sqrt{\mathrm{x-}-[\mathrm{x}]} is discontinuous, is

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Need to check at doubtful points
discont at x I only

\begin{aligned} & \text { at } x=-1 \Rightarrow f\left(-1^{+}\right)=1+0=1 \\ & \Rightarrow f\left(-1^{-}\right)=2+1=3 \\ & \text { at } x=0 \Rightarrow f\left(0^{+}\right)=0+0=0 \\ & \Rightarrow f\left(0^{-}\right)=1+1=2 \\ & \text { at } x=1 \Rightarrow f\left(1^{+}\right)=1+0=1 \\ & \Rightarrow f\left(1^{-}\right)=0+1=1 \end{aligned}

discont. at two points

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Nehul

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