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Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Mcq Single Correct #23

A function \(f\) from natural numbers to integers is defined by \(f(n)=\begin{cases}(n-1)/2,&n\text{ odd}\\-n/2,&n\text{ even}\end{cases}\). It is

✅ Step-by-Step Solution

Final Answer: Option (D): One-one and onto both
  1. For \(n=1,2,3,4,\ldots\), the images are \(0,-1,1,-2,\ldots\), each integer exactly once. Nonnegative \(k\) has preimage \(2k+1\); negative \(-k\), with \(k\ge1\), has preimage \(2k\).

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