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

Relations & Functions · Question 111 of 125

Question 111

MediumOriginal question

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

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

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$e^{x}$ is strictly increasing: one-one.
Every $y > 0$ is $e^{\log y}$ : onto $(0, \infty)$ .

Worth noting

The same $e^{x}$ is not onto $\mathbb{R}$ ; here the codomain is its exact range.

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:R→(0,∞)f : \mathbb{R} \to (0, \infty)f:R→(0,∞), f(x)=exf(x) = e^{x}f(x)=ex?

Explanation

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