Kisi Kisi PAT Matematika Kelas XI no 69

69. Fungsi f : R → R dan g : R →R didefinisikan oleh 𝑓(𝑥) = 1/2 𝑥 − 1 dan 𝑔(𝑥) = 2𝑥 + 4, maka (𝑔 ◦ 𝑓)⁻¹(10) =⋯

A. 4

B. 8

C. 9

D. 12

E. 16

Jawaban :

𝑓(𝑥) = 1/2 𝑥 − 1

𝑔(𝑥) = 2𝑥 + 4

(𝑔 ◦ 𝑓)(x)

= g (f (x))

= g ( 1/2 x - 1)

= 2(1/2 x - 1) + 4

= x - 2 + 4

= x + 2

(𝑔 ◦ 𝑓)(x) = x + 2

cari inversnya :

(𝑔 ◦ 𝑓)(x) = x + 2

y = x + 2

y - 2 = x

x = y - 2

(𝑔 ◦ 𝑓)⁻¹(y) = y - 2

(𝑔 ◦ 𝑓)⁻¹(x) = x - 2

(𝑔 ◦ 𝑓)⁻¹(10) = 10 - 2

(𝑔 ◦ 𝑓)⁻¹(10) = 8

Jawaban : B