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

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${\frac{π}{4}, \frac{3 π}{4}}$

$[\frac{π}{4}, \frac{3 π}{4}]$

None of these

$(\frac{π}{4}, \frac{3 π}{4})$

answer is C.

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Detailed Solution

$f (x) = \sin^{- 1} x + \tan^{- 1} x + \sec^{- 1} x$ , clearly domain of $f (x)$ is $x = \pm 1$

Thus, range is ${f (1), f (- 1)}$

i.e., ${\frac{π}{4}, \frac{3 π}{4}}$

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