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1 )
$f\left( x \right)=\left\{ \begin{matrix} -{{x}^{2}}+1\,\,\,\,\,\,\,\,\,\,\,\,\,x\lt 0 \\ {{x}^{2}}-1\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ge 0 \\\end{matrix} \right.$
$f\left( x \right)=\left\{ \begin{matrix} {{x}^{2}}-1\,\,\,\,\,\,\,\,\,\,\,\,\,x\le 0 \\ -{{x}^{2}}+1\,\,\,\,\,\,\,\,\,\,\,x\gt 0 \\\end{matrix} \right.$
3 )
$f\left( x \right)=\left\{ \begin{matrix} {{x}^{2}}-1\,\,\,\,\,\,\,\,\,\,\,\,\,x\gt 0 \\ -{{x}^{2}}+1\,\,\,\,\,\,\,\,\,\,\,x\ge 0 \\\end{matrix} \right.$
4 )
$f\left( x \right)=\left\{ \begin{matrix} {{x}^{2}}+1\,\,\,\,\,\,\,\,\,\,\,\,\,x\lt 0 \\ -{{x}^{2}}+1\,\,\,\,\,\,\,\,\,\,\,x\ge 5 \\\end{matrix} \right.$