Which of these describes f : R → R, f(x) = [x], the greatest integer function?

Relations & Functions · Question 121 of 125

Question 121

HardOriginal question

Which of these describes $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = [x]$ , the greatest integer function?

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

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$f(1.2) = f(1.7) = 1$ : not one-one.
Only integers are reached, so 0.5 is not: not onto.

Worth noting

Its values are integers only, so it misses most of $\mathbb{R}$ .

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

The rule this testsOnto and bijective functions

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Which of these describes f:R→Rf : \mathbb{R} \to \mathbb{R}f:R→R, f(x)=[x]f(x) = [x]f(x)=[x], the greatest integer function?

Explanation

Which of these describes $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = [x]$ , the greatest integer function?