$1-\left| x \right|=y\to \left| x \right|=1-y$
$x=\pm (1-y)\to f(y)=\sqrt{{{(\pm (1-y))}^{2}}-4}\to f(y)=\sqrt{{{y}^{2}}-2y-3}$
پس: $\sqrt{{{x}^{2}}-2x-3}\to {{x}^{2}}-2x-3\ge 0\to (x-3)(x+1)\ge 0\to \left( -\infty ,-1 \right]\bigcup \left[ 3,\infty \right)$