# Finding the domain of a composite function

by lindseyam
Tags: composite, domain, function
 P: 7 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
 HW Helper P: 3,309 start with finding the domain of g(x) and f(x)
P: 7
 Quote by lanedance 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.

HW Helper
P: 3,309

## Finding the domain of a composite function

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]

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