It is the function for which all the elements of the range of the function corresponds to exactly one element of the domain.
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Edit: It is the function for which each element of the range of the function corresponds to exactly one element of the domain.
a function is a one-to-one and many-to one relation
It means the solution (which is a function) does not have a limit on at least one side
A formula or graph are two ways to describe a math function. How a math function is described depends on the domain of the function or the complexity of the function.
If you mean 1/x (some symbols get lost in the questions), that is called the reciprocal. It means, for any given number, find a number which, when multiplied with the given number, gives 1. Or equivalently, simply one divided by the given number.
That sounds really comlicated.