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one-to-one function
[one-to-one function|one-to-one function] A one-to-one function is a function where each output corresponds to exactly one input.
Definition
one-to-one function A one-to-one function is a function where each output corresponds to exactly one input. The inverse of such a function is also a function, satisfying f -1 (f(x)) = x and f(f -1 (x)) = x.
Effects
one-to-one function shows that a relationship can fail to be one-to-one when distinct inputs produce the same output.
Examples
one-to-one function A restricted version of the square function f(x) = x² with domain limited to [0, ∞) is a one-to-one function, which passes the <a href='/en/entity/horizontal-line'>horizontal line test</a> and has an inverse (the square-root function).