Which of these describes f : Z → Z, f(n) = 2n + 1?

Relations & Functions · Question 92 of 125

Question 92

MediumOriginal question

Which of these describes $f : \mathbb{Z} \to \mathbb{Z}$ , $f(n) = 2n + 1$ ?

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

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CorrectNot quiteAnswer A

Correct answer: A

$2a + 1 = 2b + 1$ gives $a = b$ : one-one.
Every value is odd, so 4 is never reached: not onto.

Worth noting

On $\mathbb{Z}$ , $2n + 1$ reaches only the odd integers.

Concept: Classifying a function
Typical timeTypical: 90 s
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The rule this testsOne-one functions

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Which of these describes f:Z→Zf : \mathbb{Z} \to \mathbb{Z}f:Z→Z, f(n)=2n+1f(n) = 2n + 1f(n)=2n+1?

Explanation

Which of these describes $f : \mathbb{Z} \to \mathbb{Z}$ , $f(n) = 2n + 1$ ?