Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
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 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?
Thanks,
Richard
http://en.wikibooks.org/wiki/Calculus/Algebra
|
|
|
|
