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Here, [x]-x= -{x} needs to be greater than or equal to zero. But we know that {x} always lies in [0, 1) so that it's negative will lie in (-1, 0]. Since the term under square root sign can not be less than zero, hence the function will be defined only for {x}= 0. Or x belonging to integer values. Obviously the range is zero.

Dear student

 

As we know

 

[x] – x = – {x}

 

hence its value will always be negative and zero.

 

 

but it is under sqyare root sign hence it should be positive or zero.

 

hence it should be zero only.

 

hence Domain = All integer points

 

Range = 0