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

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

Prove that the function f: R rarr R defined by f(x) = 2x + 5 is one-one.

Show that the function f:N rarr N given by f(x) = 5x is one-one but not 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 : NrarrN given by f (x) = 2x is one-one but not onto.

Show that the function f: N rarrN given by f(x)= 3x is one-one but not onto.

Show that the function f : R_* rarr R_* defined by f (x) = 1/x is one-one and onto, where R_* is the set of all non-zero real numbers. Is the result true, if the domain R_* is replaced by N with co-domain being same as R_* ?

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

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

Show that the function f : R rarr R given by f (x) = x^3 is injective.