Find (f*g)(x) and its domain when f(x)=x^2+9 and g(x)= sqrt x+3

Question

A. (f·g)(x)=x+12; (-∞,∞)

B. (f·g)(x)=√x^2+12; (-∞,∞)

C. (f·g)(x)=√x^2+12; [-3,∞)

D. (f·g)(x)=x+12; [-3,∞)

I need help please. I don't know how to get the correct answer

Answer 1

f◦g = f(g) = g^2 + 9 = √(x+3)^2 + 9 = x+3 + 9 = x+12
So, it's gonna be either A or D.
But g(x) is undefined for x < 3, so ...

Answer 2

>sigh<
No. What happens if you try to take f(g(-10))?
g(-10) is undefined, so there's no way to evaluate f.

So, D is the right choice. The domain of g helps to determine the domain of f(g)