What is the range of $2\tan^{-1} x$ ?

[-\pi, \pi]

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(-\pi, \pi)

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

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(0, 2\pi)

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\tan^{-1} x$ runs over the open interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ .
Doubling gives $(-\pi, \pi)$ , still open.

Worth noting

$[-\pi, \pi]$ closes the ends, but $\tan^{-1}$ never reaches $\pm\frac{\pi}{2}$ .

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 2tan⁡−1x2\tan^{-1} x2tan−1x?