<Dd> g (y) = y + 7 5 . (\ displaystyle g (y) = (\ frac (y + 7) (5)).) </Dd> <P> With y = 5x − 7 we have that f (x) = y and g (y) = x . </P> <P> Not all functions have inverse functions . In order for a function f: X → Y to have an inverse, it must have the property that for every y in Y there must be one, and only one x in X so that f (x) = y . This property ensures that a function g: Y → X will exist having the necessary relationship with f . </P> <P> Let f be a function whose domain is the set X, and whose image (range) is the set Y . Then f is invertible if there exists a function g with domain Y and image X, with the property: </P>

When does a function have an inverse function
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