Find the Domain of the Function
Question:
The domain of definition of the function
\[ f(x)=\sqrt{x-1}+\sqrt{3-x} \]
is
(a) \([1,\infty)\)
(b) \((-\infty,3)\)
(c) \((1,3)\)
(d) \([1,3]\)
Solution:
For square roots to exist,
\[ x-1\ge0 \]
\[ x\ge1 \]
Also,
\[ 3-x\ge0 \]
\[ x\le3 \]
Therefore,
\[ 1\le x\le3 \]
Hence, the domain is
\[ \boxed{[1,3]} \]
\[ \boxed{\text{Correct Answer: (d)}} \]