Read the two statements and choose the correct option.
I. The curve $y = \sec^{-1} x$ has no points with $-1 < x < 1$ .
II. The curve $y = \cos^{-1} x$ is symmetric about the $y$ -axis.

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: $\sec^{-1}$ needs $\lvert x \rvert \ge 1$ . True.
II: $\cos^{-1}(-x) = \pi - \cos^{-1} x$ , not $\cos^{-1} x$ ; the curve is symmetric about the point $\left(0, \frac{\pi}{2}\right)$ , not the axis. False.

Worth noting

$\cos x$ is symmetric about the $y$ -axis, but its inverse is not.

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

Read the two statements and choose the correct option.I. The curve y=sec⁡−1xy = \sec^{-1} xy=sec−1x has no points with −1<x<1-1 < x < 1−1<x<1.II. The curve y=cos⁡−1xy = \cos^{-1} xy=cos−1x is symmetric about the yyy-axis.