Let F(x)=3x, g(x)= -2x^2, and h(x)=x^2-1. Evaluate each composite function 1. (FoG)(3) 2. (GoF)(1) 3. (FoF)(1)

Answer 1

Question 1
(f o g) (x) = f (- 2 x ² ) = - 6 x ²
(f o g)(3) = - 54

Question 2
(g o f) (x) = g (3 x) = - 18 x ²
(g o f)(1) = - 18

Question 3
(f o f) (x) = f (3 x) = 9 x
(f o f) (1) = 9

Answer 2

(fog)(3) = f[g(3)] = f[-2*9] = f(-18) = 3* (-18) = -54


(gof)(1) = g[f(1)]=g[3]= -18

(fof)(1)= f[f(1)] = f(3) = 9

Answer 3

(FoG)(3) = f(g(3))
So first plug in 3 for g (-2)(3)^2 = -18
Then plug (-18) into F
f(-18) = (-18)*3 = -54

GoF(1) = g(f(1))
3(1) = 3
g(3) = -2(3)^2 = -18

FoF(1) = f(f(1))
3(1) = 3
3(3) = 9

In this case the h(x) information is useless.