Function Its Own InverseDate: 01/02/98 at 22:40:07 From: Jaime Subject: Inverse function Show that f(x)= __X__ Is it's own inverse. X-1 I have tried substituting x in for y and y in for x, but I always get stuck. Date: 01/07/98 at 10:58:27 From: Doctor Jaffee Subject: Re: Inverse function Hi Jaime, It sounds to me as if you are off to a good start. Making the substitutions that you suggested will work if you then isolate the y. The result should be y = x/(x-1), which is exactly the result you need to prove that the function is its own inverse. There is another method you can use, however. If g(x) and f(x) are inverse functions, then g(f(x)) and f(g(x)) will both equal x. In this particular case, you are trying to show that a function is its own inverse, so it is sufficient to demonstrate that f(f(x)) = x. Give it a try. If you can handle complex fractions, you should be successful. Also, try graphing y = x/(x-1) and y = x on the same grid. You should notice that y = x/(x-1) is symmetrical around the line y = x. That is another way to show that the function is its own inverse. Can you figure out why these suggestions work? -Doctor Jaffee, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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