Question

What is the inverse function of `F(x) = (7/x) - 3`?

Answer 1

`F^{-1}(x)=7/(x+3)`

Explanation:

To invert an (invertible!) function `f` we can proceed as follows:

1. Introduce a dependent variable `y` defined by the expression of the function in the independent variable `x`:
   `y:=f(x)`.

2. Switch the roles of the dependent variable `x` and the independent variable `y`, trying to express `x` as a function of `y`. That function is called inverse function of `f` and it's denoted by `f^{-1}`:
   `x=f^{-1}(y)`

In our specific case, `F(x)=7/x-3`. We write
`y:=F(x)=7/x-3`
and now we solve for `x`:
`y+3=7/x`
`(y+3)/7=1/x`
`7/(y+3)=x`
We conclude that the inverse function of `F` is the function
`F^{-1}(y)=7/(y+3)`