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Range of $S i n^{- 1} x + C o s^{- 1} x + T a n^{- 1} x$ is

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$(0, \frac{π}{2})$

$(0, π]$

$[\frac{π}{4}, \frac{3 π}{4}]$

$[0, π]$

answer is C.

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Detailed Solution

$f (x) = S i n^{- 1} x + C o s^{- 1} x + T a n^{- 1} x$

$∴ C o m m o n D o m a i n = [- 1, 1]$

$∵ - 1 \leq x \leq 1$

$T a n^{- 1} (- 1) \leq T a n^{- 1} x \leq T a n^{- 1} (1)$

$\Rightarrow - \frac{π}{4} \leq T a n^{- 1} x \leq \frac{π}{4}$

$\Rightarrow \frac{π}{2} - \frac{π}{4} \leq \frac{π}{2} + T a n^{- 1} x \leq \frac{π}{2} + \frac{π}{4}$

$∴ R a n g e : [\frac{π}{4}, \frac{3 π}{4}]$

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