Finding the domain of a composite function

lindseyam

1. The problem statement, all variables and given/known data

I started out with f(x)=sinx and g(x)=1-√x. I found f(g(x)) which is sin(1-√x) and now my problem is how to find the domain. I've really been struggling with the domain part and just need this one done step by step so i have an idea of how to actually do it.

2. Relevant equations



3. The attempt at a solution

lanedance

start with finding the domain of g(x) and f(x)

lindseyam

If I knew how to get the domain I would but I'm having trouble with the domain for both parts.

lanedance

ok so whats your definition of domain?

Unless it is defined otherwise, I would informally interpret it as the region of input variable over which the function is valid

lets start with an easy but relevant example, what is the valid domain of [\itex]\mathbb{R} [/itex], for the function [\itex]h(x) = \sqrt{x}[/itex]