Question

The inverse of F(x) is a function

Answer 1

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:

${\displaystyle f(x)=y\,\,\Leftrightarrow \,\,g(y)=x$

In other words, the function $f$ is applied to an input x, and gives an outcome of y, then its inverse function, let say $g$, 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

$\:\:f\left(x\right)=b\:-x$

the inverse is:

$f^{-1}\left(y\right)=b\:-y$