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# inverse function

the function that replaces another function when the dependent and independent variables of the first function are interchanged for an appropriate set of values of the dependent variable. In y = sin x and x = arc sin y, the inverse function of sin is arc sine.
[1810-20]

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Mathematical function that undoes the effect of another function.

For example, the inverse function of the formula that converts Celsius temperature to Fahrenheit temperature is the formula that converts Fahrenheit to Celsius. Applying one formula and then the other yields the original temperature. Inverse procedures are essential to solving equations because they allow mathematical operations to be reversed (e.g. logarithms, the inverses of exponential functions, are used to solve exponential equations). Whenever a mathematical procedure is introduced, one of the most important questions is how to invert it. Thus, for example, the trigonometric functions gave rise to the inverse trigonometric functions.

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Universalium. 2010.

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• inverse function — function which is reached by expressing the dependent variable of one function as the independent variable of another (Mathematics) …   English contemporary dictionary

• inverse function — in′verse func′tion n. math. math. the function that replaces another function when the dependent and independent variables of the first function are interchanged for an appropriate set of values of the dependent variable • Etymology: 1810–20 …   From formal English to slang

• Inverse function theorem — In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain. The theorem also gives a formula for the derivative of the… …   Wikipedia