Question

Let f(x) = 4x2 + 8x + 7 and g(x) = 3x + 2. Determine the rule for the composite functions f ∘ g and g ∘ f.

(g ∘ f)(x) =

(f ∘ g)(x) =

Answer 1

(g ° f)(x) = 12x² + 24x + 23

(f ° g)(x) = 36x² + 72x + 49

Explanation:

Here we go. Firstly you have to rewrite f ° g into f(g(x)), that should make it clearer. We, then substitute every x in f by g(x). So:

f(g(x)) = 4(g(x))² + 8(g(x)) + 7

= 4(3x+2)²+8(3x+2)+7

= 4(9x²+12x+4) + 24x + 16 + 17

= 36x² + 48x + 16 + 24x + 16 + 17

finally.. you need to regroup like that:

f ° g(x) = 36x² + 72x + 49

The same thing for g ° f(x)

but this time you substitute by f(x) in g(x) instead.