Question

The inverse of F(x) is a function

Answer 1

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`