1. Let the sets be
$$
\begin{array}{l}
M=\left\{y \left\lvert\, y=x^{\frac{1}{2}}\right., x \in[1,4]\right\}, \\
N=\left\{x \mid y=\log _{2}(1-x)\right\} .
\end{array}
$$

Then $M \cap \complement_{\mathbf{R}} N=$ ( .
(A) $\{x \mid 1 \leqslant x \leqslant 2\}$
(B) $\{x \mid 1 \leqslant x \leqslant 4\}$
(C) $\{x \mid 1 \leqslant x \leqslant \sqrt{2}\}$
(D) $\varnothing$
-1. A.
Calculate that $M=[1,2], N=(-\infty, 1)$.
Thus $M \cap \complement_{\mathbf{R}} N=\{x \mid 1 \leqslant x \leqslant 2\}$.