Under what conditions is the inverse of a function a function?

Can/does this have something to do with the input and outputs of a function or is it as simple whether or not it passes the vertical line test?

Thanks!

-Tom

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- Sep 27th 2006, 02:28 PMTomCatQuick question about inverse functions.
*Under what conditions is the inverse of a function a function?*

Can/does this have something to do with the input and outputs of a function or is it as simple whether or not it passes the vertical line test?

Thanks!

-Tom - Sep 27th 2006, 03:21 PMSoroban
Hello, Tom!

Quote:

*Under what conditions is the inverse of a function a function?*

Can/does this have something to do with the input and outputs of a function

or is it as simple whether or not it passes the vertical line test?

It**is**as simple as the vertical line test.

There's an "eyeball" approach, too.

Look at the graph of the function f(x).

If it passes the "horizontal line test", its inverse is a function.

(That is, if all horizontal lines intersect the graph in at most one point,

. . then the inverse is also a function.)

- Sep 27th 2006, 04:46 PMTomCat
Thank you!

- Sep 27th 2006, 05:08 PMTomCat
- Sep 27th 2006, 05:32 PMQuick
- Sep 27th 2006, 05:33 PMThePerfectHacker
- Sep 27th 2006, 05:41 PMQuick
- Sep 27th 2006, 05:47 PMThePerfectHacker
A single point can define a function.

For example, {(1,1)}

There is a formal definition of a function that appeared in the 19th Century due to one of my favorites, Dirichlet. Ever since then people started using his definition. A single point fits this definition.

The first time the word "function" was used by the German polymath/mathematician Gottfiend von Leibniz (he was as much as a nemesis to Newton as I am to Captain**Blank**). He definied informally as a relationship between two things. For example, the size of a tree as a function of time.

When LaTeX is back online I can give you a formal treatement of what a function is in a mathematical sense. (But be warned this is going to be your first tour of pure mathematics. It might be dangerous). - Sep 27th 2006, 06:01 PMQuick