Let f(x) = sqrt(x+2) and g(x) = x^2 - 2, then find f ○ g and g ○ f.

Question

Need step by step please.

Answer 1

f(x) = √(x+2)

g(x) = x² - 2

 

f ○ g =  √(g(x)+2) = √(x²-2+2) = √x² = x

 

g ○ f = f(x)² - 2 = (√(x+2))² - 2 = x + 2 - 2 = x

 

In this case f°g = g°f, but it not generally true.