Solution for Problem 3.6.1

Let   f(x) = 3x + 2 and g(x) = 2x - 4.  Find (f ° g)(x) and  (g ° f)(x

Solve

Step

(f og)(x) = f(g(x)) = f(2x - 4)

Substitute g(x) into f(x)

              = 3(2x - 4) + 2 = 6x - 12 + 2 = 6x - 10

We have a new function 6x - 10

(g of)(x) = g(f(x)) = g(3x + 2)

Substitute f(x) into g(x)

              = 2(3x + 2) - 4 = 6x + 4 - 4 = 6x

We have a new function 6x  

Notice that 6x - 10 ¹  6x                                 (f og)(x) and  (g o f)(xmay not be equal