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Definition of Inverse - 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!

The definition of a function can be extended to define the definition of inverse of a function. Along with one to one functions, invertible functions are an important type of function. The definition of inverse says that a function's inverse switches its domain and range. The definition of inverse helps students to understand the unique characteristics of the graphs of invertible functions.

The inverse of a function. So the inverse of a function is written f little -1 of x. And careful before we go any further, I want to specify that this is not the same thing as 1 over f of x. Okay? Normally we're used to negative exponents bringing things down to the denominator. This is a different inverse. And you're told by this notation okay?
So what the inverse actually is, is the set of all points yx where xy belong to the function. What that means okay, we'll put it into more simple terms, is that if f of x has the point 3 -1, the inverse is going to have the the opposite, okay if you just flip your x and your y's. So this the y would become the x value and the x will become the y value. Okay? So the inverse is basically the set of all points so f of x is going to be a curve or have a relationship with a bunch of points. f inverse of x is going to be the set of all those points with the value switched, okay. There's no switching of sign like the -1 doesn't become opposite, it just becomes the x and y values are inverted or switched.

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