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Definition of One-to-One Functions - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

After learning the definition of a function, we can extend it to define a one to one function. A one to one function has not only one output for every input, but also only one input in the domain for every output in therange. Another interesting type is an invertible function, or a function that has an inverse. The graph of a one to one or invertible function has unique and interesting characteristics.

Earlier we talked about a function which is a relationship between x and y where for every x there is only one y. And remember we did the vertical line test to check our graphs. We looked at some tables but the main thing is for every x there is only one y.
What we're going to talk about now is a special function called the one to one function which remains a function so every x there is only one y, but it also means that for every y there is only one x. So it's the function but we throw in that extra clause for every y only one x.

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