reason for it to work, or in what way it works.
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It means that y is a function of k.
The inverse function means the opposite calculation. The inverse function of "add 6" would be "subtract 6".
It means that there is a function - which is here named with the generic name "g"; it might be any function - and that this function depends on variable "y".
That means that either the function is equal to zero everywhere (y = 0), or it is the exponential function (y = ex).
It is the function for which all the elements of the range of the function corresponds to exactly one element of the domain.