Assertion (A): The curve $y = \cos^{-1} x$ lies on or above the $x$ -axis.
Reason (R): $\cos^{-1} x$ is defined only for $-1 \le x \le 1$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

A is true: every value of $\cos^{-1}$ lies in $[0, \pi]$ , so $y \ge 0$ at every point of the curve.
R is true too, but it limits $x$ , how far the curve runs left and right; A is about $y$ and comes from the range.

Worth noting

R is the domain: it explains why the curve stops at $x = \pm 1$ , not why it stays above the $x$ -axis.

Concept: Facts about the graphs
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsGraphs of the inverse functions

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

Assertion (A): The curve y=cos⁡−1xy = \cos^{-1} xy=cos−1x lies on or above the xxx-axis.Reason (R): cos⁡−1x\cos^{-1} xcos−1x is defined only for −1≤x≤1-1 \le x \le 1−1≤x≤1.

Explanation

Assertion (A): The curve $y = \cos^{-1} x$ lies on or above the $x$ -axis.
Reason (R): $\cos^{-1} x$ is defined only for $-1 \le x \le 1$ .