Use the graphs to evaluate the expressions below fg3 gf4 f

Use the graphs to evaluate the expressions below. f(g(3)) = g(f(4)) = f(f(0)) = g(g(5)) = Let f(x) = 6x - 6 and g(x) = 7x + 3. Then (f g)(x) = (g f) (x) =

Solution

1.

A.

g(3) = 4

f(g(3)) = f(4) = 1

B.

f(4) = 1

g(f(4)) = g(1) = 0

C.

f(0) = 0

f(f(0)) = f(0) = 0

D.

g(5) = 3

g(g(5)) = g(3) = 4

2.

A.

fog(x) = f(g(x)) = f(x^2 - 7x + 3)

= 6*(x^2 - 7x + 3) - 6

= 6x^2 - 42x + 12

B.

gof(x) = g(f(x)) = g(6x - 6)

= (6x - 6)^2 - 7(6x - 6) + 3

= 36x^2 + 36 - 72x - 42x + 42 +3

= 36x^2 - 112x + 81