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)):

f (x) = 15x - 12 g (x) = - 15x^2 + 14x - 10

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)):

f (x) = - 13x^2 - 13x + 14 g (x) = - 13x - 11

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