Question

Check the continuity of f given by $f\left(x\right)=\{\begin{array}{ccc}(x^2-9)/(x^2-2x-3)& if& 0<x<5\\ 1.5& if& x=3\end{array}$ and $x\ne 3$ at the point $3$.

Answer 1

$RHL=LHL=\underset{x\to 3}{lim}\frac{x^2-9}{x^2-2x-3}=0$

value of the function at $x=3$, we have $1.5$. Hence, it is not continuous.