Question

If $f$ is continuous and $g$ is discontinuous at $x=a$, then $f\left(x\right).g\left(x\right)$ is discontinuous at $x=a.$
If true enter 1 else enter 0

Answer 1

Given statement is not true.
Example. Take $f\left(x\right)=x^2$ continuous at $x=0$ and $g\left(x\right)=\frac{|x|}{x}$ discontinuous at $x=0$
Clearly $f\left(x\right).g\left(x\right)$ is continuous at $x=0$