Question

Q1: Find f + g, f − g, fg, and f/g and their domains.
f(x) = √16 − x2, g(x) = √x + 3

a) Find (f + g)(x).

b) Find the domain of (f + g)(x).(Enter your answer using interval notation.)

c) Find (f − g)(x).

d) Find the domain of (f − g)(x).(Enter your answer using interval notation.)

e) Find (fg)(x).

f) Find the domain of (fg)(x).(Enter your answer using interval notation.)

g) Find (f/g)(x).

h) Find the domain of (f/g)(x).(Enter your answer using interval notation.)

Answer 1

Trying to deal with your lack of parentheses, I get
(f/g)(x) = f(x)/g(x) = √(16-x^2)/√(x+3)
The domain excludes x <= -3 because of the denominator
and also |x| > 4 due to the numerator. So that leaves (-3,4]

See what you can do with the rest; they are similar.