how to find range of greatest integer function and fractional function

To solve this type of problems the easiest way is to know about their graph and their domain. then plot their graph in given domain and plot the solutions (get this solution by method of sign-scheme ...etc) on the graph.  By puting the value of domain in graph you will know its RANGE easily.

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Hi Amarnath,

The [x], range is the entire set of integers (that is the definition of a gretest integer function)

Say for n≤x<n+1, then [x] = n

So for [f(x)], you need to find the range of f(x) for the given domain of f(x). If domain is not given, then you need to identify the domain of f(x) first, and then in that domain you need to find the range of f(x).

Once range of f(x) is found, then range of [f(x)], is obtained by splitting the range into intervals n≤f(x)<n+1.

For fractional part of x, the range is 0≤{x}<1.

And as mentioned above, you can find the range of {f(x)}.

All the best.

Regards,

Ashwin (IIT Madras).