Difference between revisions of "Inverse function"
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| − | In [[mathematics]], if a [[Function (mathematics)|function]] f(x)=y | + | In [[mathematics]], if a [[Function (mathematics)|function]] <code>f(x)=y</code> is [[Injective function|injective]], exactly one function <code>g(y)</code> will exist such that <code>g(y)=x</code>, otherwise no such function will exist. |
| − | The function g(y) is called the inverse function of f(x) because it "reverses" f(x); that is to say g(f(x))=x. | + | The function <code>g(y)</code> is called the inverse function of <code>f(x)</code> because it "reverses" <code>f(x)</code>; that is to say <code>g(f(x))=x</code>. |
== See also == | == See also == | ||
Latest revision as of 14:24, 8 September 2016
In mathematics, if a function f(x)=y is injective, exactly one function g(y) will exist such that g(y)=x, otherwise no such function will exist.
The function g(y) is called the inverse function of f(x) because it "reverses" f(x); that is to say g(f(x))=x.
See also
- Function (mathematics)
- Injective function
- Inverse function theorem, gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain and gives a formula for the derivative of the inverse function
- Inverse functions and differentiation
- Inverse relation
- Lagrange inversion theorem, gives the Taylor series expansion of the inverse function of an analytic function
External links
- Inverse function @ Wikipedia
