Write the domain and the range of the function,.

Given, f(x) =

Where [x] is the Greatest Integer Function of x.

f(x) =

where {x} is fractional part of x.

The graph of f(x) is

(i) dom(f)

Domain of{x} is R.

The value of the fractional part of x is always either positive or zero.

Hence domain of f(x) is R.

(ii) range(f)

Range of {x} is [0,1).

As the root value [0,1) between interval lies between [0,1).

Hence range of f(x) is [0,1).