Functions Question 89
Question: A function f from the set of natural numbers to integers defined by $ f(n)= \begin{cases} & \frac{n-1}{2},\ when\ n\ is\ odd \\ & -\frac{n}{2},\ \text{when }n\text{ is even} \\ \end{cases} . $ , is
[AIEEE 2003]
Options:
A) One-to-one but not onto
B) Onto but not one-one
C) One-to-one and onto both
D) Neither one-to-one nor onto
Show Answer
Answer:
Correct Answer: C
Solution:
$ f:N\to I $ $ f(1)=0,,f(2)=-1,,f(3)=1,,f(4)=-2,,f(5)=2 $ and $ f(6)=-3 $ so on. In this type of function every element of set A has unique image in set B and there is no element left in set B. Hence f is one-one and onto function.
BETA
