The domain of log4−x21+x is

fx=log4−x21+x is defined iff4−x2>0 and 1+x>0⇒ x2−4 −1⇒ x+2x−2 −1∴ x∈−1, 2

The domain of log4−x21+x is

fx=log4−x21+x is defined iff4−x2>0 and 1+x>0⇒ x2−4 −1⇒ x+2x−2 −1∴ x∈−1, 2

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$T h e d o m a i n o f \log (\frac{\sqrt{4 - x^{2}}}{1 + x}) i s$

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$(- 2, 2)$

$(- 1, \infty)$

$[- 1, 2]$

$(- 1, 2)$

answer is D.

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Detailed Solution

$\begin{array}{l} f (x) = \log (\frac{\sqrt{4 - x^{2}}}{1 + x}) i s d e f i n e d i f f \\ 4 - x^{2} > 0 a n d 1 + x > 0 \\ \Rightarrow x^{2} - 4 < 0 a n d x > - 1 \\ \Rightarrow (x + 2) (x - 2) < 0 a n d x > - 1 \\ ∴ x \in (- 1, 2) \end{array}$

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The domain of log4−x21+x is

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$T h e d o m a i n o f \log (\frac{\sqrt{4 - x^{2}}}{1 + x}) i s$