Finding an Inverse Function

Date: 8/28/96 at 10:38:14
From: Enzo Tantimonaco
Subject: Inverse Function

What is the inverse function -- f(-1) -- of f(x) = 1 - 2x? 
What is the general method for finding an inverse function?

Thanks in advance,
Enzo

Date: 8/30/96 at 11:0:22
From: Doctor Jerry
Subject: Re: Inverse Function

There is no general method, one which works for all possible 
functions.  Here is a method that works, IF the equation y=f(x) can be 
solved for x in terms of y .  

For the function given, 

1. Write the equation y = 1 - 2x.
2. Solve it for x in terms of y: x = (1-y)/2.
3. Since most persons want to describe all functions in terms of x, 
   interchange y and x in the result of step 2.  This gives
   y = (1-x)/2.
4. The inverse function f^(-1) is given by
    f^(-1)(x) = (1-x)/2.

It is clear that f(f^(-1)(w)) = w  and  f^(-1)(f(u)) = u.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/