Show that function `f: Rrarr R` given by `f(x) = x^2` is neither one-one nor onto.

Show that function f: Nrarr N given by f(x) = x^2 is neither one-one nor onto.

Show that function f: Zrarr Z given by f(x) = x^2 is neither one-one nor onto.

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 .

Show that the function f : R rarr R given by f(x) =x^2 is injective.

Prove that Modulus Function f: R rarr R given by : f(x) = | x | is neither one-one nor onto, where | x | is x, if x is positive and | x | is - x, if x is negative.

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

Show that the function f:N rarr N given by f(x) = 4x is one-one, but not onto.

Show that the function f:N rarr N given by f(x) = 5x is one-one but not onto.

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

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