In mathematical analysis, an inverse function is in simple terms a function which "does the reverse" of a given function.
For example, if the function x → 3x + 2 is given, then its inverse function is x → (x  2) / 3. This is usually written as:
The superscript "1" is not an exponent. Similarly, f ^{ 2}(x) means "do f twice", that is f(f(x)), not the square of f(x) (sadly, this notation has an exception for the trigonometric functions: sin^{2}(x) usually does mean the square of sin(x). As such, the prefix arc is sometimes used to denote inverse trigonometric functions[?], eg arcsin x for the inverse of sin x).
Generally, if f(x) is any function, and g is its inverse, then g(f(x)) = x and f(g(x)) = x. In other words, an inverse function undoes what the original function does.
For a function f to have a valid inverse, it must be a bijection, that is:
It is possible to work around this condition, by redefining f's codomain to be precisely its range, and by admitting a multivalued function as an inverse.
If one represents the function f graphically in an xy coordinate system, then the graph of f ^{1} is the reflection of the graph of f across the line y = x.
Algebraically, one computes the inverse function of f by solving the equation
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