If $f(x)=\frac{1}{(x-2)(2x-5)}$ and $g(x)=\frac{1}{{x}^{2}}$ , we define f(g(x)) over the domain in which its defined , is it correct to say f(g(x)) is discontinuous at $+-\surd (2/5)$ ,0 and +-$1/\surd 2$ ? 0 because the input is going into g(x) hence as its not in domain of g(x) so it can be said its discontinuous at that point . and similarily other four points as its not in domain of f(g(x)) ? But if suppose we say h(x)=f(g(x)) will we say h(x) is discontinuous at those points (maybe different ones) where x is not defined after simplyfing the whole f(g(x)) to a rational function ?