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

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

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

Show that the function f : R to R , defined by f(x) = 1/x is one-one and onto, where R, is the set of all non-zero real numbers.

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

Prove that the Greatest Integer Function f: R to R, 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 Modulus function f : R to R given by f (x) = [x] is neither one-one nor onto.

Prove that the function f: R to R defined by f(x) = 4x + 3 is invertible and find the inverse of 'f' .

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

Show that the Modulus Functions f : R to R, given by f (x) =|x|, is neither one-one nor onto, whre |x| is x, if x is positive or 0 and |x| is -x, if x is negative.