JEE Main 2003 — Functions Question with Solution
From: AIEEE 2003
Question
A function from the set of natural numbers to integers defined by
$f\left( n \right) = \left\{ {\matrix{
{{{n - 1} \over 2},\,when\,n\,is\,odd} \cr
{ - {n \over 2},\,when\,n\,is\,even} \cr
} } \right.$
is
Choose an option
Show full solutionCorrect option: D
Correct answer
Done-one and onto both
Step-by-step explanation
We have
If and are two even natural numbers,
then
Again if and are two odd natural numbers then
is onto.
Also each negative integer is an image of even natural number and each positive integer is an image of odd natural number.
is onto.
Hence is one one and onto both.
If and are two even natural numbers,
then
Again if and are two odd natural numbers then
is onto.
Also each negative integer is an image of even natural number and each positive integer is an image of odd natural number.
is onto.
Hence is one one and onto both.
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This is a previous-year question from JEE Main 2003, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.