On the set of integers $Z$. define $f: Z \to Z$ as $ f(n) =
\begin{cases}
n/2 & \quad \text{if } n \text{ is even}\\
0 & \quad \text{if } n \text{ is odd}\\
\end{cases}
$ then $'f'$ is
- bijective
- injective but not surjective
- neither injective nor suijective
- surjective but not injective
The Correct Option is D
Solution and Explanation
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Concepts Used:
Types of Functions
Types of Functions
One to One Function
A function is said to be one to one function when f: A → B is One to One if for each element of A there is a distinct element of B.
Many to One Function
A function which maps two or more elements of A to the same element of set B is said to be many to one function. Two or more elements of A have the same image in B.
Onto Function
If there exists a function for which every element of set B there is (are) pre-image(s) in set A, it is Onto Function.
One – One and Onto Function
A function, f is One – One and Onto or Bijective if the function f is both One to One and Onto function.
Read More: Types of Functions