f(x) = x/(x+4) Yes you need parentheses; otherwise it's x/x + 4 = 1 + 4 = 5. You can't divide by zero, so we cannot have x+4 = 0. Thus x = -4 is excluded from the domain. All other values of x are included.
y = √(13+x). You can't take the square root of negative numbers, so we must have 13+x ≥ 0, so the domain is x ≥ -13.
P(x) = -2x2 + 40x -34. I added the x2, which I think you intended to put into the problem but left out. This is a quadratic equation. The domain is all real numbers.