Fungsi f: R⇒R dan g: R⇒R dirumuskan dengan f(x) = 2x-1 dan g (x) = 3x+5, maka (g o f) min 1 (a) =-2. Nilai a adalah?

◾ Materi : Invers
◾ Sub materi : Fungsi Invers
◾ Mapel : Matematika
◾ Keyword : Invers Fungsi, Invers Fungsi Komposisi

ㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡ

Jawab :
f(x) = 2x-1
g(x) = 3x+5

(gof)(x) = 3(2x-1) + 5
(gof)(x) = 6x-3+5
(gof)(x) = 6x+2

(gof)(x) = 6x+2
y = 6x+2
6x = y-2
x = 1/6 (y-2)
(gof)-¹(x) = 1/6 (x-2)

(gof)-¹(a) = 1/6 (a-2)
-2 = 1/6 (a-2)
-12 = a-2
a = -12+2
a = -10

Jadi, nilai a adalah -10

semoga membantu
# sharing is caring #
-vin

Mapel : Matematika
Materi : Fungsi
Kelas : 10, 11
===================

f(x) = 2x - 1
g(x) = 3x + 5
(g o f) -¹(a) = -2

Ditanya → Nilai a = __?
Jawaban :
________

(g o f) (x) = g(2x - 1)
(g o f) (x) = 3(2x - 1) + 5
(g o f) (x) = 6x - 3 + 5
(g o f) (x) = 6x + 2

Untunk invers (g o f) (x), misalkan
6x + 2 = y
6x = y - 2
x = (y - 2)/6

Maka,
(g o f) -¹(x) = (x - 2)/6

Nilai a adalah ;

(x - 2)/6 = - 2
(x - 2) = - 2(6)
x - 2 = -12
x = -12 + 2
x = -10

Sehingga a = x = -10 ⏩