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.

2. 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.
The easiest way of getting the maximal domain is to get the rule for f(g(x)):

$f(g(x)) = \sqrt{g(x) - 16} = \sqrt{(5 - x) - 16} = \sqrt{-x - 11}$. You should be able to get the maximal domain of this.

3. The domain of f(x) is $x-16 \geq 0$

The domain of g(x) is all real numbers

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

$-x -11 \geq 0$

$-x \geq 11$

$x \leq -11$

Edit: posted to late