A function f from the set of natural numbers to integers defined by f(n)=begincases(n-1)/(2),&textwhen ntext is odd\\-frac n2,&textwhen ntext is evenendcases is

Functions: A function f from the set of natural numbers to integers defined by… | AIEEE 2003

AIEEE 2003 (Offline)Question 1

A function $f$ from the set of natural numbers to integers defined by $f(n)=\begin{cases}\frac{n-1}{2},&\text{when }n\text{ is odd}\\-\frac n2,&\text{when }n\text{ is even}\end{cases}$ is

Functions

neither one-one nor ontoone-one but not ontoonto but not one-oneone-one and onto both✓ Correct answer

Solution

Odd $n=2k+1$ gives $k=0,1,2,\dots$; even $n=2k$ gives $-k=-1,-2,\dots$. Each integer is hit exactly once, so $f$ is one-one and onto.

Functions - JEE Mathematics question (AIEEE 2003 (Offline))

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