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Relations & Functions · Question 110 of 125

Question 110

MediumOriginal question

Which of these describes f:R−{0}→R−{0}f : \mathbb{R} - \{0\} \to \mathbb{R} - \{0\}, f(x)=1xf(x) = \frac{1}{x}?

Options for question 110

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. 1a=1b\frac{1}{a} = \frac{1}{b} gives a=ba = b: one-one.

  2. Any non-zero yy is f(1y)f\left(\frac{1}{y}\right): onto.

Worth noting

With 0 removed from both sides, 1x\frac{1}{x} undoes itself, so it is a bijection.

Concept
Classifying a function
Typical time
90 s
Your time
—
The rule this testsOnto and bijective functions
Practise this chapter →

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

Practise this chapter →

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