## afievans 10 months ago Find the domain of the composite function f∘g. f(x)=x^2+2; g(x)=√x−1

1. sleung

The domain is the set of all reals, since f(g(x))=x+1.

2. afievans

why is f(g(x)) = x+1 since the equation states f(g(x)) equals the square root of x-1

3. sleung

You plug in the square root of x-1 for x.

4. sleung

$f(g(x))=(\sqrt{x-1})^{2}+2=(x-1)+2=x+1$

5. afievans

oh great... this makes sense now. so what is the domain? hope I am asking the right question

6. sleung

x can be anything, so the domain is the set of all real numbers.

7. afievans

Thank you. you are a star!