Inverse function

An inverse function is a concept of mathematics. A function will calculate some output $y$, given some input $x$. This is usually written $f(x)=y$. The inverse function does the reverse. Let's say $g()$ is the inverse function of $f()$, then $g(y)=x$. Or otherwise put, $f(g(x))=x$. An inverse function to $f(\ldots )$ is usually called $f^{-1}(\ldots ).$ Do not confuse $f^{-1}(\ldots )$ with $f(\ldots )^{-1}$: the first is a value of an inverse function, the second is reciprocal of a value of a normal function.

Examples

Let's take a function $f(x)=x^{3}$ over real $x$. Then, $f^{-1}(x)={\sqrt[{3}]{x}}.$

At first, make $y=f(x)$to $x=f(y)$. For example $y=e^{x}$ to $x=e^{y}$, It also $\ln x=y$, so It's inverse function is $y=\ln x$.

Not all functions have inverse functions: for example, function $f(x)=|x|$ has none (because $|-1|=1=|1|$, and $f^{-1}(x)$ should give both 1 and -1 when given 1)), but every binary relation has its own inverse relation.

Finding the inverse of a function can be very difficult to do.

See also

• Inverse triangle function
• Inverse hyperbolic function