What is the domain of tan^-1(1/x)?

Inverse Trigonometric Functions · Question 9 of 120

Question 9

EasyOriginal question

What is the domain of $\tan^{-1}\left(\frac{1}{x}\right)$ ?

\mathbb{R}

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\mathbb{R} - (-1, 1)

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(0, \infty)

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\mathbb{R} - \{0\}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\tan^{-1}$ accepts every real number, so the only condition is that $\frac{1}{x}$ exists.
That needs $x \ne 0$ : the domain is $\mathbb{R} - \{0\}$ .

Worth noting

$\mathbb{R}$ is the domain of $\tan^{-1}$ itself; the inner $\frac{1}{x}$ must be defined first.

Ten questions from Inverse Trigonometric Functions, at your own pace.

Ten questions from Inverse Trigonometric Functions, at your own pace.