Prove that the greatest integer function defined by `f(x) = [x], 0

Find all the points of discontinuity of the greatest integer function defined by f(x) = [x] where [x] denotes the greatest integer less than or equal to x.

Prove that greatest integer function f: RrarrR , given by f (x) = [x] , is neither one-one nor onto where [x] denotes the greatest integer less than or equal to x .

Let f : R to R be the signum function defined as f(x) = {{:(1, x gt 0),(0, x =0),(-1, x lt 0):} and g: R to R be the greatest integer function given by g(x) = [x] where [x] is greatest integer less than or equal to x. Then, does fog and gof coincide in (0,1] ?

Let [] donots the greatest integer function and f (x)= [tan ^(2) x], then

Prove that the greatest integer function [x] is continuous at all points except at integral points.

f(x)= cosec^(-1)[1+sin^(2)x] , where [*] denotes the greatest integer function. then range of f(x) is

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

f(x)=log(x-[x]) , where [*] denotes the greatest integer function. find the domain of f(x).

Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuous function at x= 1.