consider this function [tex]f(x)=[x[\frac{1}{x}]][/tex] ([x] represent greatest integer less than or equal to x or in short GIF )(adsbygoogle = window.adsbygoogle || []).push({});

internal brackets over 1/x and external brackets are around full body of function.

discuss on these points(means either are these correct incorrect)

Statement 1:this function is discontinuous at infinitely points.

Statement 2:this function is discontinuous for infinitely many points for x belongs to (0,1)

I think both statements are correct.

Put x=1/10. It will give 1. but if I put 1/(10.1).1 it will give zero. So it's discontinuous function. similarly we can say that it is discontinuous at infinitely many points between 0 to 1.

If second statement is correct than first will definitely correct...

when result from internal GIF will smaller than 1/x it will give zero, else output should 1.

am i correct?

if not then where am i wrong.

Is there any way to solve such questions on wolframalpha

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# What about continuity and discontinuity of this function?

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