A. Evaluate the following showing steps as indicated in the lesson content.

1. f(x) = 15x – 12 and g(x) = -15x^2 + 14x - 10
find g(f(7))

2. f(x) = -13x^2 - 13x + 14 and g(x) = -13x - 11
find g(g(3))

1) g(f(7)) is -128443 and

2) g(g(3)) is -661

Step-by-step explanation:

1) find g(f(7)) :

Step 1 :

To find f(7), substitute x=7 in the given f(x),

f(7) = 15(7) – 12

f(7) = 105 - 12

f(7) = 93

Step 2 :

To find g(f(7)), substitute f(7)=93 in the given g(x),

g(f(7)) = -15(93)²+14(93)-10

⇒ -129735 + 1302 -10

⇒ -129745 + 1302

⇒ -128443

Therefore, g(f(7)) = -128443

2) find g(g(3)) :

Step 1 :

To find g(3), substitute x=3 in the given g(x),

g(3) = -13(3) - 11

g(3) = -39 - 11

g(3) = 50

Step 2 :

To find g(g(3)), substitute g(3)=50 in the given g(x),

g(g(3)) = -13(50) -11

⇒ -650 -11

⇒ -661

Therefore, g(g(3)) = -661