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Define each of the following:
(i) bijective function
(ii) many – one function
Give an example of each type of functions.

Solution:

(i)Bijective function: It is, also known as one-one
onto function and is a function where for every element of set A, there is exactly one image in set B, such that no element is set B is left
without match or ordered pair.
For example: $f: R \rightarrow R$ given by $f(x) = 3x + 8$ for all $x \in R$ is a bijection function.

(ii) Many-one function: It is is function where for
image in Set B, there is more than one element in Set A.
For example: $f: Z \rightarrow Z$ defined by $f(x) = x^2 + x + 1$ for all $x \in Z$