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Inverse Function

# Inverse Function - Definition of Inverse of a Function Let...

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Definition of Inverse of a Function Let f and g be two functions such that f ( g ( x )) = x , for every x in the domain of g g ( f ( x )) = x , for every x in the domain of f , then the function g is said to be the inverse of the function f and is denoted . The domain of f is equal to the range of and the range of f is the domain of . Example 1 : Use the definition of inverse functions to determine if the functions f and g are inverses of each other: and . Let’s look at f ( g ( x )) first: *Insert the "value" of g inside the function of f *Plug in the "value" of g wherever there is an x the function f

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Next, let’s look at g ( f ( x )): *Insert the "value" of f inside the function of g *Plug in the "value" of f wherever there is an x the function g Since f ( g ( x )) AND g ( f ( x )) BOTH came out to be x , this proves that the two functions are inverses of each other. Example 2 : Use the definition of inverse functions to determine if the functions f and g are inverses of each other: and . Let’s look at f ( g ( x )) first: *Insert the "value" of g inside the function of f *Plug in the "value" of g wherever there is an x the function f Since BOTH f ( g ( x )) AND g ( f ( x )) would have to equal x for them to be inverses of each other and f ( g ( x )) is not equal to x , then we can stop here and say without a doubt that they are NOT inverses of each other .
The Horizontal Line Test for Inverse Functions If NO horizontal line can be drawn so that it intersects a graph of a function f more than once, then the function f has an inverse function The next two examples illustrate this concept. Example 3

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Inverse Function - Definition of Inverse of a Function Let...

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