If $f(x) = 2x$ and $g(x) = \frac{{{x^2}}}{2} + 1,$ then which of the following can be a discontinuous function?

We know that, if $f$ and $g$ be continuous functions, then
$f + g$ is continuous

$f - g$ is continuous.

$fg$ is continuous

$\frac{f}{g}$ is continuous at these points, where $g(x) \ne 0$.

Here, $\frac{{g(x)}}{{f(x)}} = \frac{{\frac{{{x^2}}}{2} + 1}}{{2x}} = \frac{{{x^2} + 2}}{{4x}}$
which is discontinuous at $x = 0$