We can view a function as something that maps things of
one type to things of another type. The inverse of a function tells you how to get back
to the original value. We do this a lot in everyday life, without really thinking about
it.
For example, think of a sports team. Each
player has a name and a number. So if you knew a players name and wanted to know their
number, you could think of this as a function from players to their numbers. Now, if you
wanted to do the reverse, find a players name given their number, you would be using the
inverse of this function.
Another example:
suppose I am travelling at 60 miles per hour, and want to know how far I have gone in x
hours. Then this could be represented by the function`f(x) = 60 *
x`
Now I want to know the inverse: If I know I
have travelled x miles how long have I been travelling for? `f^{-1}(x) =
x/60`
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