Solución

limx1f(x)\mathop {\lim }\limits_{x \to 1} f\left( x \right) no existe porque limx1f(x)=2limx1+f(x)=2\mathop {\lim }\limits_{x \to {1^ - }} f\left( x \right) = - 2 \ne \mathop {\lim }\limits_{x \to {1^ + }} f\left( x \right) = 2