Book: RS Aggarwal - Mathematics
Chapter: 3. Functions
Subject: Maths - Class 11th
Q. No. 11 of Exercise 3F
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11
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).
