Finding an Inverse FunctionDate: 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/ |
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