Finding the domain of a composite function

[lindseyam]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[lanedance]

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

 

[lindseyam]

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

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

 

[lanedance]

ok so what's 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]