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

1 Answer

F^{-1}(x)=7/(x+3)F1(x)=7x+3

Explanation:

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

  1. Introduce a dependent variable yy defined by the expression of the function in the independent variable xx:
    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)