(i) One-One (Injective):
If is said to be one-one i.e., &
(ii) Onto (Surjective):
If is said to be onto i.e., .
(iii) One-one & Onto (Bijective):
If is said to be bijective i.e., is both injective & surjective i.e., one-one correspondence
A function is said to be a many-one function, if two or more elements of have the same image in .
Thus is many one if for , but .
If is into such that at least one element in codomain which is not the image of any element is domain.
Hence have no pre-image in .