Inverse Function - Real-world Examples

Real-world Examples

For example, let ƒ be the function that converts a temperature in degrees Celsius to a temperature in degrees Fahrenheit:

then its inverse function converts degrees Fahrenheit to degrees Celsius:

since

Or, suppose ƒ assigns each child in a family its birth year. An inverse function would output which child was born in a given year. However, if the family has twins (or triplets) then the output cannot be known when the input is the common birth year. As well, if a year is given in which no child was born then a child cannot be named. But if each child was born in a separate year, and if we restrict attention to the three years in which a child was born, then we do have an inverse function. For example,

\begin{align} f(\text{Allan})&=2005, \quad & f(\text{Brad})&=2007, \quad & f(\text{Cary})&=2001 \\ f^{-1}(2005)&=\text{Allan}, \quad & f^{-1}(2007)&=\text{Brad}, \quad & f^{-1}(2001)&=\text{Cary} \end{align}

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