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# Definition of One-to-One Functions - Concept

###### 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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###### Carl Horowitz

B.S. in Mathematics University of Michigan

He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his step-by-step explanations are easy to follow.

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