What is the range of $\tan^{-1} x$ ?

\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

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\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]

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(0, \pi)

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\mathbb{R}

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CorrectNot quiteAnswer A

Correct answer: A

$\tan$ is one-one on $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ and takes every real value there.
The ends are left out: $\tan \frac{\pi}{2}$ is not defined.

Worth noting

The closed interval wrongly takes in $\pm\frac{\pi}{2}$ , where $\tan$ has no value.

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

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

What is the range of tan⁡−1x\tan^{-1} xtan−1x?