a) Assertion is True, Reason is True, Reason is a correct explanation for Assertion
b) Assertion is True, Reason is True, Reason is not a correct explanation for Assertion
c) Assertion is True, Reason is False.
d) Assertion is False, Reason is True.
Assertion : The domain of
$f (x) = e^{2 x} + \cos^{- 1} (\frac{x}{2} - 1) + \log \sqrt{(x)},$ is $(0, 1) \cup (1, 2) \cup (2, 3) \cup (3, 4)$
Reason : The domain of $\cos^{- 1} (\frac{x}{2} - 1)$ is (0,4).

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answer is D.

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Detailed Solution

$\cos^{- 1} x$ is defined for $- 1 \leq x \leq 1$

$- 1 \leq \frac{x}{2} - 1 \leq 1 \Rightarrow 0 \leq \frac{x}{2} \leq 2 \Rightarrow 0 \leq x \leq 4$

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