[tex]\it f(x)\leq x \Rightarrow x\sqrt2+2\leq x \Rightarrow x\sqrt2-x\leq-2 \Rightarrow x(\sqrt2-1)\leq-2\bigg|_{\cdot(\sqrt2+1)} \Rightarrow \\ \\ \Rightarrow x\leq-2\sqrt2-2 \Rightarrow x\in(-\infty,\ \ -2\sqrt2-2][/tex]
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[tex]\it f(x)\leq x \Rightarrow x\sqrt2+2\leq x \Rightarrow x\sqrt2-x\leq-2 \Rightarrow x(\sqrt2-1)\leq-2\bigg|_{\cdot(\sqrt2+1)} \Rightarrow \\ \\ \Rightarrow x\leq-2\sqrt2-2 \Rightarrow x\in(-\infty,\ \ -2\sqrt2-2][/tex]