If f(x) = [x] , 0<= {x} < 0.5 and f(x) =...

If `f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 ` then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

Similar Questions

Explore conceptually related problems

If f(x) = {(2x,0 lt=xlt=a),(0,"otherwise"):} is a probability density function of a random variable then the value of a is ……….. .

Prove theat the greatest interger function defined by f(x)= |x|, 0 lt x lt 3 is not differentiable at x=1 and x= 2.

Find the derivative of f(x) = 3 at x = 0 and at x = 3.

If f(x)={{:(2x, 0 le x le a), (0, "otherwise"):} is a probability density function of a random variable, then the value of a is

If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)| then

If f(x)={x-2, x le 0 and 4-x^2,x > 0, then discuss the continuity of y=f(f(x)).

Given f'' (x) = 6x + 6 , f'(0) = -5 and f(1) = 6 find f(x) .

Discuss the continuity of the function f given by f(x)= |x|" at "x=0 .