Explanation:
a. f(g(0)) = f(0^2 - 2) = f(-2) = -2 + 3 = 1
b. g(f(0)) = g(0+3) = g(3) = 3^2 - 2 = 7
c. f(g(x)) = g(x) + 3 = x^2 - 2 + 3 = x^2 + 1
d. g(f(x)) = f(x)^2 - 2 = (x+3)^2 - 2 = x^2 + 6x + 7
e. f(f(-2)) = f(-2+3) = f(1) = 1+3 = 4
f. g(g(4)) = g(4^2 - 2) = g(14) = 14^2 - 2 = 194
g. f(f(x)) = f(x+3) = (x+3)+3 = x+6
h. g(g(x)) = g(x^2 - 2) = (x^2 - 2)^2 -2 = x^4 - 4x^2 + 2