Inverse function

In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function. More formally, if f is a function with domain X, then f −1 is its inverse function if and only if for every x in X we have:

Related Topics:
Mathematics - Function

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:f^{-1}(f(x))=f(f^{-1}(x))=x.,

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For example, if the function x → 3x + 2 is given, then its inverse function is x → (x−2) / 3. This is usually written as:

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: fcolon x o 3x+2

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: f^{-1}colon x o(x-2)/3

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The superscript "−1" is not an exponent. Similarly, as long as we are not in trigonometry, f 2(x) means "do f twice", that is f(f(x)), not the square of f(x). For example, if : f : x → 3x + 2, then f 2 : x = 3 ((3x + 2)) + 2, or 9x + 8. However, in trigonometry, for historical reasons, sin2(x) usually does mean the square of sin(x). As such, the prefix arc is sometimes used to denote inverse trigonometric functions, e.g. arcsin x for the inverse of sin(x).

Related Topics:
Trigonometry - Inverse trigonometric function

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