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Relations & Functions · Question 72 of 125

Question 72

EasyOriginal question

Which of these describes f:R→Rf : \mathbb{R} \to \mathbb{R}, f(x)=3x−5f(x) = 3x - 5?

Options for question 72

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. 3a−5=3b−53a - 5 = 3b - 5 gives a=ba = b: one-one.

  2. For any yy, x=y+53x = \frac{y + 5}{3} gives f(x)=yf(x) = y: onto.

Worth noting

A non-constant linear function on R\mathbb{R} is a bijection.

Concept
Classifying a function
Typical time
60 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.