An injective function f has a well-defined partial inverse f − 1. If y is an element of the image set of f, then there is at least one input x such that f(x) = y. If f is injective then this x is unique and we can define f − 1(y) to be this unique value. We have f − 1(f(x)) = x for all x in the domain.
A strictly monotonic function is injective, since in this case x1 < x2 implies that f(x1) < f(x2) (if f is increasing) or f(x1) > f(x2) (if f is decreasing).
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