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

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

The function is g(x) = (1/2)*(e^(-x)) x is R

Thank you!!!!

2. ## Re: Determine if the function is a contraction! Thank you!

Use the mean value theorem.

3. ## Re: Determine if the function is a contraction! Thank you!

What happens as x goes to $-\infty$? For it to be a contraction, $|g'(x)|$ has to be less than 1, right?

- Hollywood

4. ## 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?

5. ## 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, $0\le{c}<1$ such that $|g(x)-g(y)|\le{c}|x-y|$ for all $x,y\in\mathbb{R}$ where $g(x)$ and $g(y)$ 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