# 7: The Inverse of a Function

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• 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

This page titled 7: The Inverse of a Function is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.