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Consider the function h(x) = $f(g(x)) = \frac{3}{\frac{6}{3-x}}$ from $g(x) = \frac{6}{3-x}$ and $f(x) = \frac{3}{x}$ , we will say that h(x) to be not defined at infinity and -infinity as both those points make the denomiator of h(x) to be zero ? So there will be three points where h(x) is not defined at $\infty , - \infty$ and $3 $? Or does the set of real numbers always exclude the infinity points so we dont take it into conideration ?

ProblemDestroyer
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    $\def\bfr{\mathbf{R}}$There is no such thing called "infinity" in the set $\bfr$ of real numbers. One may consider the extended real number line though. And it does not make sense to say "domain of ... is not defined". –  May 04 '22 at 17:27
  • Okay so real numbers do not include those points hence we dont need to worry at all regarding those points ? While in case of extended real line we would have to exclude thosr two points ? @user1046533 – ProblemDestroyer May 04 '22 at 17:32
  • Yes. 2. It depends very much on what you really want to do with the functions you have. Purely formal manipulation of those things is not very interesting (at least for me...)
    • –  May 04 '22 at 17:37
  • Alright thanks a lot – ProblemDestroyer May 04 '22 at 18:38