Which of these describes f : R → R, f(x) = e^x?

Relations & Functions · Question 119 of 125

Question 119

HardOriginal question

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

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

$e^{x}$ is strictly increasing, so it is one-one.
$e^{x} > 0$ always, so 0 and negatives are not reached: not onto.

Worth noting

The range of $e^{x}$ is $(0, \infty)$ , smaller than the codomain $\mathbb{R}$ .

Concept: Classifying a function
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsOnto and bijective functions

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Which of these describes f:R→Rf : \mathbb{R} \to \mathbb{R}f:R→R, f(x)=exf(x) = e^{x}f(x)=ex?

Explanation

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