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Domain
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 ⇔ f (x) = y
for any y in B.