Prove that `f(x)= [x^2] -[x]^2` is discontinuous for all integral values of x except only at `x=1`.

Show that f(x) = x-[x] is discontinuous for integral values of x

Prove that f (x) = [X] is discontinuous for integral values of x.

Show that the function f(x) = [x]^(2) - [x^(2)] is discontinuous at all integers except 1

Prove that, f(x) =x+2+(x-2)e^(x) is positive for all positive values of x.

If f:RR rarr RR is a function defined by f(x)=[x]cos((2x−1)/2)pi where [x] denotes the greatest integer function, then f is (1) continuous for every real x (2) discontinuous only at x=0 (3) discontinuous only at non-zero integral values of x (4) continuous only at x=0 .

Prove that f(x)={((x-|x|)/x, x!=0),( 2 , x=0):} is discontinuous at x=0 .

The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is the greatest integer less than or equal to gamma ), is discontinuous at a. all integers b. all integers except 0 and 1 c. all integers except 0 d. all integers except 1

Proved that: f(x)=[x\ if\ x in Q1-x\ if\ x !in Q\ is continuous only at x=1//2.

Statement-1: The function f(x)=[x]+x^(2) is discontinuous at all integer points. Statement-2: The function g(x)=[x] has Z as the set of points of its discontinuous from left.

Statement-1: The function f(x)=[x]+x^(2) is discontinuous at all integer points. Statement-2: The function g(x)=[x] has Z as the set of points of its discontinuous from left.