Question

find g^4(x) and the domain and range of g(x) and g^4(x)
1. g(x) = 9 - x^2, x< 0
2. g(x) = (x - 1)^2 +1, x<1

Answer 1

well, you have given the domains. In each case, g(x) is the left side of a parabola. g^4(x) is a similar graph, but with a flatter vertex. Compare the graphs of x^2 and x^8.

#1.
g(x) < 9
g^4(x) < 9^4

#2
g(x) > 1
g^4(x) > 1