Find the Domain of the Function
The domain of definition of
\[ f(x)= \sqrt{x-3-2\sqrt{x-4}} – \sqrt{x-3+2\sqrt{x-4}} \]
is
(a) \([4,\infty)\)
(b) \((-\infty,4]\)
(c) \((4,\infty)\)
(d) \((-\infty,4)\)
For the inner square root,
\[ x-4\ge0 \]
\[ x\ge4 \]
Also,
\[ x-3-2\sqrt{x-4} = (\sqrt{x-4}-1)^2\ge0 \]
and
\[ x-3+2\sqrt{x-4} = (\sqrt{x-4}+1)^2\ge0 \]
Hence, all expressions are defined for
\[ x\ge4 \]
Therefore, domain is
\[ \boxed{[4,\infty)} \]
\[ \boxed{\text{Correct Answer: (a)}} \]