f(x)=x^2-2 and g(x)=sqrt(x+1) find (f o g) and (g o f)
(f o g) is the same as f(g())
So, f(g(x)) = g(x)^2 - 2 = [sqrt(x + 1)]^2 - 2 = (x + 1) - 2 = x - 1
(g o f) is the same as g(f())
So, g(f(x)) = sqrt(f(x) + 1) = sqrt(x^2 - 2 + 1) = sqrt(x^2 - 1)
Answer: (f o g) = x - 1, (g o f) = sqrt(x^2 - 1)