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Relations & Functions · Question 91 of 125

Question 91

MediumOriginal question

Which of these describes f:R→Rf : \mathbb{R} \to \mathbb{R}, f(x)=x2+2xf(x) = x^{2} + 2x?

Options for question 91

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. f(−2)=f(0)=0f(-2) = f(0) = 0: not one-one.

  2. x2+2x=(x+1)2−1≥−1x^{2} + 2x = (x + 1)^{2} - 1 \ge -1, so −2-2 is never reached: not onto.

Worth noting

A quadratic on R\mathbb{R} is never one-one, and never onto R\mathbb{R}.

Concept
Classifying a function
Typical time
90 s
Your time
—
The rule this testsOne-one functions
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Ten questions from Relations & Functions, at your own pace.

Practise this chapter →

Ten questions from Relations & Functions, at your own pace.