The figure shows the graph of a function defined only on [-1, 1], rising from (-1, -π/2) to (1, π/2). Which function is it? A curve rising from (−1, −π/2) to (1, π/2)

The figure shows the graph of a function…

The figure shows the graph of a function defined only on [-1, 1], rising from (-1, -π/2) to (1, π/2).

Question 65

EasyOriginal question

The figure shows the graph of a function defined only on $[-1, 1]$ , rising from $\left(-1, -\frac{\pi}{2}\right)$ to $\left(1, \frac{\pi}{2}\right)$ . Which function is it?

A curve rising from (−1, −π/2) to (1, π/2)

y = \cos^{-1} x

Correct answerYour answer

y = \tan^{-1} x

Correct answerYour answer

y = \sin x

Correct answerYour answer

y = \sin^{-1} x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Domain $[-1, 1]$ and values from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ , rising.
That is $\sin^{-1} x$ , the mirror image of $\sin x$ on $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ in the line $y = x$ .

Worth noting

$\sin x$ itself is defined for every $x$ and takes values only in $[-1, 1]$ : the roles of the axes are swapped.

Concept: Recognising an inverse function from its graph
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsGraphs of the inverse functions

Practise this chapter →

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

Practise this chapter →

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

The figure shows the graph of a function defined only on [-1, 1], rising from (-1, -π/2) to (1, π/2).

Question 65

Explanation