• Sep 17th 2008, 01:19 PM
gobbajeezalus
Hi everyone, I've been having trouble with finding the domain of composite functions. Can somebody please solve this problem for me? I think I have the answer but I'm not sure.
http://img.skitch.com/20080917-e4t3d...u8mnin3tbi.jpg
• Sep 17th 2008, 01:33 PM
mr fantastic
Quote:

Originally Posted by gobbajeezalus
Hi everyone, I've been having trouble with finding the domain of composite functions. Can somebody please solve this problem for me? I think I have the answer but I'm not sure.
http://img.skitch.com/20080917-e4t3d...u8mnin3tbi.jpg

The easiest way of getting the maximal domain is to get the rule for f(g(x)):

$\displaystyle f(g(x)) = \sqrt{g(x) - 16} = \sqrt{(5 - x) - 16} = \sqrt{-x - 11}$. You should be able to get the maximal domain of this.
• Sep 17th 2008, 01:35 PM
11rdc11
The domain of f(x) is $\displaystyle x-16 \geq 0$

The domain of g(x) is all real numbers

The domain of f(g(x)) = $\displaystyle \sqrt{-x -11}$ is

$\displaystyle -x -11 \geq 0$

$\displaystyle -x \geq 11$

$\displaystyle x \leq -11$

Edit: posted to late