The figure shows the graph of a function defined for every real x, passing through the origin and rising between the lines y = -π/2 and y = π/2 without reaching them. Which function is it? A curve rising through the origin between the dashed lines y = −π/2 and y = π/2

The figure shows the graph of a function…

The figure shows the graph of a function defined for every real x, passing through the origin and rising…

Question 73

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The figure shows the graph of a function defined for every real $x$ , passing through the origin and rising between the lines $y = -\frac{\pi}{2}$ and $y = \frac{\pi}{2}$ without reaching them. Which function is it?

A curve rising through the origin between the dashed lines y = −π/2 and y = π/2

y = \tan^{-1} x

Correct answerYour answer

y = \cot^{-1} x

Correct answerYour answer

y = \sin^{-1} x

Correct answerYour answer

y = \tan x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Defined for every real $x$ with values in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ : that is $\tan^{-1}$ .
It passes through the origin, since $\tan^{-1} 0 = 0$ .

Worth noting

$\cot^{-1} x$ is also defined everywhere, but it falls, between 0 and $\pi$ , and $\cot^{-1} 0 = \frac{\pi}{2}$ .

Concept: Recognising an inverse function from its graph
Typical timeTypical: 90 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 for every real x, passing through the origin and rising…

Question 73

Explanation