# Determine if the function is a contraction! Thank you!

• Feb 2nd 2013, 09:57 AM
jack56890
Determine if the function is a contraction! Thank you!
The function is g(x) = (1/2)*(e^(-x)) x is R

Thank you!!!!
• Feb 2nd 2013, 10:12 AM
emakarov
Re: Determine if the function is a contraction! Thank you!
Use the mean value theorem.
• Feb 2nd 2013, 06:38 PM
hollywood
Re: Determine if the function is a contraction! Thank you!
What happens as x goes to $\displaystyle -\infty$? For it to be a contraction, $\displaystyle |g'(x)|$ has to be less than 1, right?

- Hollywood
• Feb 3rd 2013, 11:41 AM
HallsofIvy
Re: Determine if the function is a contraction! Thank you!
Actually, there are several different ways to define "contraction". jack56890, what definition are you using?
• Feb 3rd 2013, 09:01 PM
hollywood
Re: Determine if the function is a contraction! Thank you!
My definition is that a function is a contraction if there is a real number c, $\displaystyle 0\le{c}<1$ such that $\displaystyle |g(x)-g(y)|\le{c}|x-y|$ for all $\displaystyle x,y\in\mathbb{R}$ where $\displaystyle g(x)$ and $\displaystyle g(y)$ are defined. Just so that you can put my post in context - if you're using a different definition, my post might not make sense.

- Hollywood