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}.

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

All one-one function are onto functions

Show that the function f:N to N defined by f(x)=2x-1 is one-one but not onto.

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.

Show that the function f:N toN defined by f(m)=m^(2)+m+3 is one-one function.

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 (1) =f (2) =1 and f (x) =x -1, for every x gt 2, is onto but not one-one.