Step-by-step explanation:
Let f be a function having domain in the set X, and range in the set Y. Then f would be invertible if there exists a function g having domain Y and range X, such as:
[tex]{\displaystyle f(x)=y\,\,\Leftrightarrow \,\,g(y)=x[/tex]
In other words, the function [tex]f[/tex] is applied to an input x, and gives an outcome of y, then its inverse function, let say [tex]g[/tex], can be applied to y to give the result of x.
In other words,
y = f(x) if and only if x = g(y)
For example, considering the function
[tex]\:\:f\left(x\right)=b\:-x[/tex]
the inverse is:
[tex]f^{-1}\left(y\right)=b\:-y[/tex]
