The function $f(x) = \left\{\begin{matrix} \frac{x^2+2x-3}{x-1} & x ≠ 1\\2 & x=1\end{matrix}\right.$ is :

continuous at x=1 only discontinuous at x=1 only continuous at every real number discontinuous at every real number

discontinuous at x=1 only

The correct answer is Option (2) → discontinuous at x=1 only $f(1)=2$ $\lim\limits_{x→1}\frac{x^2+2x-3}{x-1}=\lim\limits_{x→1}\frac{(x-1)(x+3)}{(x-1)}$ $=\lim\limits_{x→1}x+3=4≠2$ discontinuous at $x=1$