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Inverse Functions

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Inverse Functions

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Inverse Functions

Inverse Functions

Inverse Functions

Every one-to-one function f has an inverse function f-1 which essentially reverses the operations performed by f.

More formally, if f is a one-to-one function with domain D and range R, then its inverse f-1 has domain R and range D. f-1 is related to f in the following way: If f (x) = y, then f-1(y) = x. Written another way, f-1(f (x)) = x.


Example: f (x) = 3x - 4. Find f-1(x).

The procedure for finding f-1(x) from f (x) involves first solving for x in terms of y.


y = 3x - 4  
x =  

Now switch the variables x and y in the equation to generate the inverse:


y =  
f-1(x) =  

A function and its inverse are related geometrically in that they are reflections about the line y = x:

Figure %: A function and its inverse are symmetric with respect to the line y = x

Thus, if (a, b) is a point on the graph of f, then (b, a) is a point on the graph of f-1.

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