The figure shows the graph of a function defined for every real x, falling through (0, π/2) between the lines y = 0 and y = π without reaching them. Which function is it? A curve falling through (0, π/2) between the x-axis and the dashed line y = π

The figure shows the graph of a function…

The figure shows the graph of a function defined for every real x, falling through (0, π/2) between the…

Question 74

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The figure shows the graph of a function defined for every real $x$ , falling through $\left(0, \frac{\pi}{2}\right)$ between the lines $y = 0$ and $y = \pi$ without reaching them. Which function is it?

A curve falling through (0, π/2) between the x-axis and the dashed line y = π

y = \tan^{-1} x

Correct answerYour answer

y = \cos^{-1} x

Correct answerYour answer

y = \frac{\pi}{2} + \tan^{-1} x

Correct answerYour answer

y = \cot^{-1} x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Defined everywhere, with values in $(0, \pi)$ , and falling: that is $\cot^{-1}$ .
It crosses the $y$ -axis at $\cot^{-1} 0 = \frac{\pi}{2}$ .

Worth noting

$\frac{\pi}{2} + \tan^{-1} x$ has the same range, but it rises.

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, falling through (0, π/2) between the…

Question 74

Explanation