Give an example of a function which is
(i) neither one – one nor onto
(ii) onto but not one – one.

Solution:

(i) Neither one-one nor onto
given by
For One-one

Therefore, it is not one-one.
For Onto
We know that is always non-negative. So, there won’t be any element in domain for which is negative.
Therefore, it is not onto.
Hence, is neither one-one nor onto.

(ii) Onto but not one-one
from the set of Real numbers to the Set of Whole numbers.
For one-one

and is a real number, so can be positive or negative)
Therefore, it is not one-one.
For onto
Every element is set of Real numbers will have a value in set of Whole numbers, as a result, it is onto.