$\begin{array}{l}
Voi\,x \ge 1\,thi\,y = \frac{1}{x}\,luon\,xac\,dinh.\\
Voi\,x < 1\,thi\,y = \sqrt {x + 1} \,xac\,dinh\,khi\,x + 1 \ge 0 \Leftrightarrow x \ge - 1\\
Do\,do\,trong\,nua\,khoang\,\left[ { - 1;1} \right)\,thi\,ham\,so\,xac\,dinh.\\
Vay\,f\left( x \right)\,xac\,dinh\,tren\,D = \left[ {1; + \infty } \right) \cup \left[ { - 1;1} \right) = \left[ { - 1; + \infty } \right)\\
Chon\,C
\end{array}$