(3) $a>\sqrt{2}$ or $0<a<1$
(3) Given the function $f(x)=\frac{a}{a^{2}-2}\left(a^{x}-a^{-x}\right)(a>0$ and $a \neq 1)$ is an increasing function on $\mathbf{R}$, find the range of values for $a$.

 untranslated part:
 已知函数 $f(x)=\frac{a}{a^{2}-2}\left(a^{x}-a^{-x}\right)(a>0$ 且 $a \neq 1)$ 是 $\mathbf{R}$ 上的增函数, 求 $a$ 的取值范围.

 translated part:
 Given the function $f(x)=\frac{a}{a^{2}-2}\left(a^{x}-a^{-x}\right)(a>0$ and $a \neq 1)$ is an increasing function on $\mathbf{R}$, find the range of values for $a$.