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

Relations & Functions · Question 106 of 125

Question 106

MediumOriginal question

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

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

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

On $[0, \infty)$ , $a^{2} = b^{2}$ gives $a = b$ : one-one.
Negative numbers are not reached: not onto.

Worth noting

Cutting down the domain removes the repeats; the codomain still has numbers never reached.

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

Explanation

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