what is the domain and range of1) [x] [ ] represents greatest integer function2) {x} { } represents fractional part

The domain of both greatest integer function and fractional part is x because they can take all the values of x.

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

Say for n≤x<n+1, then [x] = n

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.

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