Problem 1: Find the domain of the function given by :

Solution :

Statement of the problem : The function has rational form. Denominator consists of product of two greatest integer functions.

We can consider, the function as product of three individual functions :

The domain of "x" is “R”. We, now, analyze individual greatest integer functions such that it does not become zero. If we recall the graph of greatest integer function, then we can realize that the value of greatest integer [x] is equal to zero for the interval given by 0≤ x < 1. Following this clue, we find the intervals in which greatest integer functions are zero.

Greatest integer function |
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For

It means that given function is undefined for this interval of “x”. The domain of the function for this condition is :

Similarly, for

The domains for this condition is :

Hence, domain of the given function is intersection of two domains as shown in the figure. Note that we have not considered the domain of numerator, “x”, as its domain is “R” and its intersection with any interval is interval itself.

Domain of the function |
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