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Topic: Question defining what exactly is a function (
Replies: 3   Last Post: Dec 1, 2010 11:54 AM

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Registered: 11/30/10
Question defining what exactly is a function (
Posted: Nov 30, 2010 10:28 AM
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I just joined the forum, I hope I can contribute something..eventually...

So I'm just re-learning calculus and trying to understand the definitions given in the the Calculus wikibook under "Calculus>>Pre-calculus>>Functions>>domain and range>>one-to-one 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 1-1 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 1-1 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?


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