Explain fractional part of x with graph.

Approach to solve greatest integer function of x and fractional part of x; (i) Let [x] and {x} represent the greatest integer and fractional part of x; respectively Solve 4{x}=x+[x]

If [x] and {x} represetnt the integral and fractional parts of x , respectively, then the value of sum_(r=1)^(1000)({x+r})/(1000) is

The function f(x)= cos ""(x)/(2)+{x} , where {x}= the fractional part of x , is a

If {x} denotes fractional part of x then {(2^(2003))/(17)} is

2[x]+ 3 {x} = x [.]=G, I. F. and {-) = fractional part of x then no. of values of x

If {x} denotes the fractional part of x, then lim_(xrarr1) (x sin {x})/(x-1) , is

If f(x) = 2^(|x|) where [x] denotes the fractional part of x. Then which of the following is true ?

The domain of f(x)=(1)/(sqrt(-x^(2)+{x})) (where {.} denotes fractional part of x) is

The domain of f(x)=sqrt(x-2{x}). (where {} denotes fractional part of x ) is

The domain of f(x)=log_(e)(1-{x}); (where {.} denotes fractional part of x ) is