1. The range of the function $y=\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1-x^{2}}+1}$ is
$\begin{array}{l}\text { I. } 1 .[1, \sqrt{2}] . \\ \text { Let } \sqrt{1+x}+\sqrt{1-x}=t>0 \text {. Then } \\ t^{2}=2+2 \sqrt{1-x^{2}} \\ \Rightarrow t^{2} \in[2,4] \Rightarrow t \in[\sqrt{2}, 2] \\ \Rightarrow y=\frac{2 t}{t^{2}}=\frac{2}{t} \in[1, \sqrt{2}] .\end{array}$