h(x) = g(f(x)) = g(x^{2} + 2x) = = |x + 1|
This bit is very important, and often overlooked.
= 3, not ±3
If x^{2} = 9, then x can be ±3, but is only +3.
So, = |x|, not +x, not ±x
Domain of |x + 1| = ( -∞, +∞), x can take any value.
As far as the range is concerned, |x + 1| cannot be negative. So, range = [0, ∞)
Correct Answer: Domain: ( -∞, +∞), Range -[0, ∞]