1. Let [ $x$ ] represent the greatest integer less than or equal to $x,\{x\}=x-[x] \sqrt{2}=1.414$ and $\sqrt{3}=1.732$. If $f(x)=\left\{x+\left[\frac{x}{1+x^2}\right]\right\}$ is a real valued function, then $f(\sqrt{2})+f(-\sqrt{3})=$

If the range of the function $f(x)=-3 x-3$ is $\{3,-6,-9,-18\}$, then which one of the following is not in the domain of $f$ ?

If $f(x)=(x+1)^2-1, x \geq-1$, then $\left\{x \mid f(x)=f^{-1}(x)\right\}$ is