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The domain of a function is the set (or area) in which all input to the function must fall.


Example 1

The domain of a logarithm is all positive real numbers ( 0, ∞ ). You can extend the domain of a logarithm to negative and complex numbers.


Example 2

One of the fundamental theorems of topology says that a simple closed curve in the plane divides this plane into exactly two domains.


Example 3

A one-to-one function f with domain A and range B has an inverse function that is defined by f −1 with domain B and range A, so

f  − 1(x) = x          ⇔          (x) = y

for any y in B.


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