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Question defining what exactly is a function (re.wiki)?
Posted:
Nov 30, 2010 10:28 AM


I just joined the forum, I hope I can contribute something..eventually...
So I'm just relearning calculus and trying to understand the definitions given in the the Calculus wikibook under "Calculus>>Precalculus>>Functions>>domain and range>>onetoone functions".
After reading the entire section on Functions, are the following conclusions valid:
************************************************** f(x)=+/?x is not a function since it does not pass the vertical line test. And therefore is not qualified for 11 or inverse.
f(x)=?x passes the vertical line test and is therefore a function. It also passes the horizontal line test for it is 11 and has an inverse. It?s inverse finction is f^1(x) = x^2.
If we then try to take the inverse of the inverse function just mentioned, we get f(x)=+/?x, which is not a valid function since it fails the vertical line test. **************************************************
Are these statements correct?
Thanks, Richard http://en.wikibooks.org/wiki/Calculus/Algebra



