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