Which of these describes f : N → N, f(n) = (n + 1)/2 for odd n and f(n) = n/2 for even n?

Relations & Functions · Question 117 of 125

Question 117

HardOriginal question

Which of these describes $f : \mathbb{N} \to \mathbb{N}$ , $f(n) = \frac{n + 1}{2}$ for odd $n$ and $f(n) = \frac{n}{2}$ for even $n$ ?

Onto but not one-oneCorrect answerYour answerOne-one and ontoCorrect answerYour answerNeither one-one nor ontoCorrect answerYour answerOne-one but not ontoCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$f(1) = 1$ and $f(2) = 1$ : not one-one.
Any $m$ is $f(2m)$ : onto.

Worth noting

Each $m$ is hit twice, by $2m - 1$ and $2m$ .

Concept: Classifying a function
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsOnto and bijective functions

Practise this chapter →

Ten questions from Relations & Functions, at your own pace.

Practise this chapter →

Ten questions from Relations & Functions, at your own pace.

Practise this chapter All 125 questions in Relations & Functions Revise the notes for Relations & Functions

Which of these describes f:N→Nf : \mathbb{N} \to \mathbb{N}f:N→N, f(n)=n+12f(n) = \frac{n + 1}{2}f(n)=2n+1​ for odd nnn and f(n)=n2f(n) = \frac{n}{2}f(n)=2n​ for even nnn?

Explanation

Which of these describes $f : \mathbb{N} \to \mathbb{N}$ , $f(n) = \frac{n + 1}{2}$ for odd $n$ and $f(n) = \frac{n}{2}$ for even $n$ ?