# 7: The Inverse of a Function


• 7.1: One-to-one functions
We have seen that some functions f may have the same outputs for different inputs. For example for f(x)=x², the inputs x=2 and x=−2 have the same output f(2)=4 and f(−2)=4 . A function is one-to-one, precisely when this is not the case.
• 7.2: Inverse function
A function is one-to-one, when each output is determined by exactly one input. Therefore we can construct a new function, called the inverse function, where we reverse the roles of inputs and outputs.
• 7.3: Exercises

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