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  • The set of all points for which<img alt="\mathrm{ f(x)=\lfloor x \mid\lfloor x-1 \mid+ 1 /[x+1]([x]}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20f%28x%29%3D%5Clfloor%20x%20

The set of all points for which\mathrm{ f(x)=\lfloor x \mid\lfloor x-1 \mid+ 1 /[x+1]([x]} is the greatest integer function) is continuous is
 

Option: 1

\mathrm{R}


Option: 2

\mathrm{R}-\mathrm{I}


Option: 3

\mathrm{R} \sim(\mathrm{I} \cup(-1,0))


Option: 4

none of these


Answers (1)

best_answer

Modulus function is continuous, [x] is continuous on  \mathrm{\mathrm{R}-\mathrm{I} ~and~ [x+1]=0~ for~ -1 \leq x<0. ~So ~\mathrm{f}}is continuous on \mathrm{R} \sim(\mathrm{I} \cup(-1,0)).

Posted by

Gautam harsolia

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