First slide

Introduction to ITF

Question

The range of $f (x) = \sin^{- 1} x + \tan^{- 1} x + \sec^{- 1} x$ is

Easy

A

$(\frac{π}{4}, \frac{3 π}{4})$
B

$[\frac{π}{4}, \frac{3 π}{4}]$
C

$\{\frac{π}{4}, \frac{3 π}{4}\}$
D

None of these

Solution

$f (x) = \sin^{- 1} x + \tan^{- 1} x + \sec^{- 1} x$ ; clearly, the domain of $f (x)$ is $x = \pm 1$ .
Thus the range is
$\{f (1), f (- 1)\} = \{\frac{π}{4}, \frac{3 π}{4}\} .$

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