Which of these describes f : R → R, f(x) = x^2?

Relations & Functions · Question 75 of 125

Question 75

EasyOriginal question

Which of these describes $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = x^{2}$ ?

Neither one-one nor ontoCorrect answerYour answerOne-one but not ontoCorrect answerYour answerOnto but not one-oneCorrect answerYour answerOne-one and ontoCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$f(-2) = f(2) = 4$ : not one-one.
No real $x$ has $x^{2} = -1$ : not onto.

Worth noting

Squaring loses the sign and never gives a negative number.

Concept: Classifying a function
Typical timeTypical: 60 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)=x2f(x) = x^{2}f(x)=x2?

Explanation

Which of these describes $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = x^{2}$ ?