Find the Domain and Range of the Function
The domain and range of the real function
\[ f(x)=\sqrt{x-1} \]
are given by
(a) Domain \(=(1,\infty)\), Range \(=(0,\infty)\)
(b) Domain \(=[1,\infty)\), Range \(=(0,\infty)\)
(c) Domain \(=[1,\infty)\), Range \(=[0,\infty)\)
(d) Domain \(=[1,\infty)\), Range \(=[0,\infty)\)
For square root function,
\[ x-1\ge0 \]
\[ x\ge1 \]
Therefore, domain is
\[ [1,\infty) \]
Also,
\[ \sqrt{x-1}\ge0 \]
Minimum value is \(0\) at \(x=1\).
Hence, range is
\[ [0,\infty) \]
Therefore,
\[ \boxed{\text{Correct Answer: (c)}} \]