Find the Domain of the Function
Question:
The domain of definition of
\[ f(x)=\sqrt{4x-x^2} \]
is
(a) \(R-[0,4]\)
(b) \(R-(0,4)\)
(c) \((0,4)\)
(d) \([0,4]\)
Solution:
For square root function,
\[ 4x-x^2\ge0 \]
\[ x(4-x)\ge0 \]
Therefore,
\[ 0\le x\le4 \]
Hence, the domain is
\[ \boxed{[0,4]} \]
\[ \boxed{\text{Correct Answer: (d)}} \]