QJEEM21Ma0243: JEE Main 2021 Mathematics - Class 12 JEEM21Ma0243 Solution: The domain of the function f ( x ) = sin − 1 ( 3 x 2 + x − 1 (…

Question

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The domain of the function

f (x) = \sin^{- 1} (\frac{3 x^{2} + x - 1}{{(x - 1)}^{2}}) + \cos^{- 1} (\frac{x - 1}{x + 1})

is :

Accepted Answer

f (x) = \sin^{- 1} (\frac{3 x^{2} + x - 1}{{(x - 1)}^{2}}) + \cos^{- 1} (\frac{x - 1}{x + 1})

- 1 \leq \frac{x - 1}{x + 1} \leq 1 \Rightarrow 0 \leq x < \infty

.... (1)

- 1 \leq \frac{3 x^{2} + x - 1}{{(x - 1)}^{2}} \leq 1 \Rightarrow x \in [\frac{- 1}{4}, \frac{1}{2}] \cup {0}

.... (2)

(1) & (2)

\Rightarrow

Domain =

[\frac{1}{4}, \frac{1}{2}] \cup {0}

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