Inverse function
function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa. i.e., f(x) = y if and only if g(y) = x From Wikipedia, the free encyclopedia
An inverse function is a concept of mathematics. A function will calculate some output , given some input . This is usually written . The inverse function does the reverse. Let's say is the inverse function of , then . Or otherwise put, . An inverse function to is usually called .[1] It is not to be confused with , which is a reciprocal function.[2]
Examples
If over real , then
To find the inverse function, swap the roles of and and solve for . For example, would turn to , and then . This shows that the inverse function of is .
Not all functions have inverse functions: for example, function has none (because , and cannot be both 1 and -1), but every binary relation has its own inverse relation.
In some cases, finding the inverse of a function can be very difficult to do.
Related pages
- Inverse element
- Inverse triangle function
- Inverse hyperbolic function
- Invertible matrix
- Reciprocal
References
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