1. If the function $f(x)=a x^{2}-\sqrt{2}$, where $a$ is a positive constant, and if $f(f(\sqrt{2}))=-\sqrt{2}$, then $a=(\quad)$
A. $\frac{2-\sqrt{2}}{2}$
B. $2-\sqrt{2}$
C. $\frac{\sqrt{2}}{2}$
D. $\frac{2+\sqrt{2}}{2}$
1. C $f(\sqrt{2})=2 a-\sqrt{2}, f(f(\sqrt{2}))=a(2 a-\sqrt{2})^{2}-\sqrt{2}=-\sqrt{2}, a=\frac{\sqrt{2}}{2}(a>0)$