1. Let the set $M=\left\{y \left\lvert\, y=x^{\frac{1}{2}}\right., x \in[1,4]\right\}, N=\left\{x \mid y=\log _{2}(1-x)\right\}$, then $M \cap\left(\complement_{\mathbf{R}} N\right)=$
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. $\varnothing$
$M=[1,2], \mathrm{C}_{\mathbf{R}} N=[1,+\infty) \Rightarrow M \cap\left(\complement_{\mathbf{R}} N\right)=[1,2]$, so the answer is $A$.