Which of these describes f : R → [0, ∞), f(x) = x^2?

Relations & Functions · Question 104 of 125

Question 104

MediumOriginal question

Which of these describes $f : \mathbb{R} \to [0, \infty)$ , $f(x) = x^{2}$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Every $y \ge 0$ is $f(\sqrt{y})$ : onto.
But $f(-1) = f(1)$ : not one-one.

Worth noting

Shrinking the codomain to $[0, \infty)$ makes $x^{2}$ onto, but not one-one.

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

The rule this testsOnto and bijective functions

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Which of these describes f:R→[0,∞)f : \mathbb{R} \to [0, \infty)f:R→[0,∞), f(x)=x2f(x) = x^{2}f(x)=x2?

Explanation

Which of these describes $f : \mathbb{R} \to [0, \infty)$ , $f(x) = x^{2}$ ?