Express the function h ( x ) = ( x + 3 ) 2 in the form f ∘ g . If f ( x ) = x 2 , find the function g ( x ) .

Answer 1

h(x) = (x+3)^2 = f(g(x))

f(x) = x^2, find g(x)

f(g(x)) = x^2 = h(x) = (x+3)^2

x^2 = (x+3)^2 = x^2 +6x +9

6x +9 =0

x =-9/6=-3/2

g(x) = -3/2

f(g(x))= f(-3/2) = (-3/2)^2 = 9/4 = (-3/2+3)^2 = (3/2)^2

g(x) =-3/2 = - 1.5