Which of these describes f : R → R, f(x) = x^3?

Relations & Functions · Question 83 of 125

Question 83

MediumOriginal question

Which of these describes $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = x^{3}$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$a^{3} = b^{3}$ gives $a = b$ : one-one.
Every real $y$ has the real cube root $\sqrt[3]{y}$ : onto.

Worth noting

Unlike $x^{2}$ , the cube keeps the sign, so it is one-one.

Concept: Classifying a function
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsOne-one functions

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Which of these describes f:R→Rf : \mathbb{R} \to \mathbb{R}f:R→R, f(x)=x3f(x) = x^{3}f(x)=x3?

Explanation

Which of these describes $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = x^{3}$ ?