Show that a one-one function `f: {1,2,3} to {1,2,3}` must be onto.

Show that an onto function f: {1,2,3} to {1,2,3} is always one-one.

Let f:{1,2,3} to {a,b,c} be one-one and onto function given by f (1) =a, f (2) =b and f (3) =c. Show that there exists a function g : {a,b,c} to {1,2,3} such that gof =I _(x) and fog =I _(y), where, X = {1,2,3} and Y={a,b,c}.

Find the number of all one-one functions from set A = {1,2,3} to itself.

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 {x in R : -1 lt x lt 1} defined by f (x) = (x)/(1 + |x|), x in R is one one and onto function.

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 toR. defined as f (x) =x ^(2), is neither one-one nor onto.

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