If mapping `f:A -> B` is one-one onto, then prove that mapping `f^-1:B -> A` is also one-one onto.

If mapping f:A rarr B is one-one onto,then prove that mapping f^(-1):B rarr A is also one- one onto.

If f:X rarr Y and g:Y rarr Z are two one-one onto mappings then prove that gof:X rarr Z is also one-one and onto mapping.

If x={1,-1} and mapping is defined as f:X rarr X,f(x)=x^(2), then prove that this mapping is not one-one onto.

Prove that the function f:A rarr B is one-one onto,then the inverse function f^(-1):B rarr A is unique.

If a function f: A to B is both one-one and onto then f is called a____.

Give an example of a map Which is not one - one but onto

f:N^2 rarr N , f(m,n)=m+n then f: [A] f is one-one, onto [B] f is one-one, not onto [C] f is onto, not one-one [D] neither one-one nor onto

Let f : A rarr B, g : B rarr C be two functions such that gof is one-one and onto. Show that f is one-one and g is onto.

Give an example of a map Which is one - one but not onto

Show that, the mapping f:NN rarr NN defined by f(x)=3x is one-one but not onto