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

Relations & Functions · Question 90 of 125

Question 90

MediumOriginal question

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

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

$f'(x) = 3x^{2} + 1 > 0$ , so $f$ is strictly increasing: one-one.
It runs from $-\infty$ to $\infty$ without a break: onto.

Worth noting

An odd-degree polynomial that only rises takes every real value exactly once.

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)=x3+xf(x) = x^{3} + xf(x)=x3+x?

Explanation

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