[tex] \lim_{x \to 1} f(x)\\f(x)= \[\begin{cases}5x-11&x\ \textless \ 1\\ 1&x=1\\-3x+6&x\ \textgreater \ 1\end{cases}\] \\ \lim_{x \to 1^-} f(x)=5(1)-11=5-11=-6\\f(1)=1\\ \lim_{x \to 1^+} f(x)=-3(1)+6=-3+6=3[/tex]
Since, [tex]\lim_{x \to 1^-} f(x)\neq\lim_{x \to 1^+} f(x)\neq f(1)[/tex]
Therefore, the limit of f(x) as x tends to 1 does not exist.
