$\def\arraystretch{1.25} \begin{array}{rcll} f\left( x\right)&=&g\left(\mathrm x\right)&\\- x^2+1&=& ax^2- a&\vert+ a\vert+ x^2\\1+\ a&=& x^2\left(1+\ a\right)&\vert:\left(1+ a\right)\\ x^2&=&1&\vert\sqrt{}\\ x&=&\pm1&\end{array}$