Question

Mapel : Matematika
Materi : Relasi dan Fungsi


Jika fungsi f(x) = 3x³ - 2x² + 2x + 1 dan g(x + 6) = 5x + 2

Tentukan
a] (f o g) -¹(x)
b] (f o g) -¹(1)

Answer 1

diket:
f(x) = 3x³ - 2x² + 2x + 1
g(x + 6) = 5x + 2
ditanya:
a) (fog)-'(x) = ...
b) (fog)-'(1) = ...

jawab:
g(x + 6) = 5x + 2, subs x->x-6
g((x-6) + 6) = 5(x-6) + 2
g(x) = 5x - 28

a) fog = f(g) = 3g³ - 2g² + 2g + 1
= 3(5x - 28)³ - 2(5x - 28)² + 2(5x - 28) + 1

b) (fog)-'(1) = m
↔ fog(m) = 1
3(5m - 28)³ - 2(5m - 28)² + 2(5m - 28) + 1 = 1
↔ (5m - 28) = 0
↔ m = 28/5

(fog)-'(1) = 28/5

maaf kl salah