Show that `f : N rarr N` given by
`f(x) = { ((x +1), if x is odd), ((x - 1), if x is even) :}`
is both one-one and onto.

Show that the signum function f : R rarr R given by f(x)= {(1,if x gt 0), (0, if x = 0), (-1, if x lt 0) :} is neither one-one nor onto.

If f : R rarr R be given by f(x) = (3 - x^3)^(1/3) , then (f o f) (x) is

Show that f: R rarr R defined by f(x) = (x-1) (x-2) (x-3) is surjective but not injective

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

Show that f:[-1,1]toR given by f(x)=frac(x)(x+2) is one-one.

Show that f:[-1,1]toR given by f(x)=frac(x)(x+2) is one-one.

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

If the function f :R rarr A given by f(x) = x^2/(x^2+1) is surjection , then find A.