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
