The function $f(x)=\frac{x}{(x-2)(x-3)(x-5)}, x \in R$ is

discontinuous at x = 2, 3, 5

The correct answer is Option (3) → discontinuous at x = 2, 3, 5

$f(x)=\frac{x}{(x-2)(x-3)(x-5)},x∈R$

∴ for $x=2,3,5$, $f(x)$ = Not defined and hence this function will be discontinuous at $x=2,3,5$.

(LHL = RHL = f(x) → Condition for continuity)

Apart from $x=2,3,5$, $f(x)$ is continuous everywhere as $f(x)$ is a polynomial.