SOLUTION: If f(x) = (x-7)/x, find f^-1(x). So basically, I need help finding the inverse of this function. I know the basic rules and the main four steps to find an inverse of a function,

Algebra ->  Functions -> SOLUTION: If f(x) = (x-7)/x, find f^-1(x). So basically, I need help finding the inverse of this function. I know the basic rules and the main four steps to find an inverse of a function,       Log On


   

Question 906484: If f(x) = (x-7)/x, find f^-1(x).
So basically, I need help finding the inverse of this function.
I know the basic rules and the main four steps to find an inverse of a function, but I keep getting stuck on this problem. I would like to see each step for solving this problem, thanks!
Please help, and thanks again in advanced!
(This is the first time I've used this website.)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The given funcgtion, f%28x%29+=+%28x-7%29%2Fx

Let g(x) be the inverse of f(x). This means g%28f%28x%29%29=f%28g%28x%29%29=x

Without staying with the fancy formal method, just switch f and x, but call the FUNCTION you
are looking for, as g.

%28g-7%29%2Fg=x
g-7=g%2Ax
-7=g%2Ax-g
g%2Ax-g=-7
g%28x-1%29=-7
g=-7%2F%28x-1%29
More formally although some of the formality was not used that way,
highlight%28f%5E-1%28x%29=-7%2F%28x-1%29%29