What is the output of a function which is not defined for input = 0 (for example because of the division by zero) if we give zero to this function? [closed]

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My teacher told me that every function has to be able to assign an output to every input we give to this function. What is than an output for a function which is not defined in zero? Nothing? Or do mathematicians say that it is a convention to say that it returns NOT DEFINED?

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1 Answer

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It is not defined since $f(x)$ is defined if and only if $x$ belons to the domain of $f$. When your teacher says “every input”, it is implicit that it is every input from the domain of $f$.

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