What is the range of $f(x) = \sin^{-1} x + \cos^{-1} x$ ?

\left[-\frac{\pi}{2}, \frac{3\pi}{2}\right]

Correct answerYour answer

[0, \pi]

Correct answerYour answer

\left[0, \frac{\pi}{2}\right]

Correct answerYour answer

\left\{\frac{\pi}{2}\right\}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ at every $x$ of the domain, $-1 \le x \le 1$ .
So $f$ takes the single value $\frac{\pi}{2}$ : its range is $\left\{\frac{\pi}{2}\right\}$ .

Worth noting

$\left[-\frac{\pi}{2}, \frac{3\pi}{2}\right]$ adds the two ranges as if the terms could be chosen apart; they move together, one up as the other goes down.

Concept: The range of a sum of inverse functions
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsDomains and ranges

Practise this chapter →

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

What is the range of f(x)=sin⁡−1x+cos⁡−1xf(x) = \sin^{-1} x + \cos^{-1} xf(x)=sin−1x+cos−1x?

Explanation

What is the range of $f(x) = \sin^{-1} x + \cos^{-1} x$ ?