Home : Support : Online Help : Math Apps : Functions and Relations : Basic Functions and Relations : MathApps/OneToOneFunction
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One-to-One Function
In order for the function $f\left(x\right)$ to be invertible, the problem of solving $x\=f\left(y\right)$ for $y$ must have a unique solution. This is because for the inverse to be a function, it must satisfy the property that for every input value in its domain there must be exactly one output value in its range; the inverse must satisfy the vertical line test. Since the domain of the inverse is the range of $f\left(x\right)$ and the range of the inverse is the domain of $f\left(x\right)$, this means that in order for $f\left(x\right)$ to be invertible, its graph must satisfy the horizontal line test: Each horizontal line through the graph of $y\=f\left(x\right)$ must intersect that graph exactly once.
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