Prove that the Greatest Integer Function `f : R->R ,`given by `f (x) = [x]`, is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

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

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

Show that the function f: R rarr R , defined as f(x) = x^2 , is neither one-one nor onto.

Show that the function defined by g(x)= x - [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

Prove that the function f :R rarr R , given by f(x) = 2x, is one-one and onto.

The number of solutions of |[x]-2x|=4, "where" [x]] is the greatest integer less than or equal to x, is

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.

Show that the function f:N rarr N , given by f(x) = 2x, is one-one but not onto.