Kisi Kisi PAT Matematika Kelas XI no 149

149. Diketahui fungsi f(𝑥) = (1 − 6𝑥) / (1 − 2𝑥) , 𝑔(𝑥) = 𝑥^2 − 3𝑥 + 6 , dan ℎ(𝑥) = 2𝑥 + 3 . Tentukan (ℎ ∘ 𝑔 ∘ 𝑓)(1)

a. 15

b. 25

c. 35

d. 45

e. 55

Jawaban :

f(𝑥) = (1 − 6𝑥) / (1 − 2𝑥)

𝑔(𝑥) = 𝑥^2 − 3𝑥 + 6

ℎ(𝑥) = 2𝑥 + 3

(ℎ ∘ 𝑔 ∘ 𝑓)(1)

= h (g (f (1)))

sehingga perlu dihitung f(1) terlebih dahulu

f(1) = (1 − 6(1)) / (1 − 2(1))

f(1) = (1 - 6) / (1 - 2)

f(1) = - 5 / - 1

f(1) = 5

(ℎ ∘ 𝑔 ∘ 𝑓)(1)

= h (g (f (1)))

= h (g (5))

sehingga perlu dihitung g(5)

𝑔(5) = (5)^2 − 3(5) + 6

g(5) = 25 - 15 + 6

g(5) = 10 + 6

g(5) = 16

selanjutnya,

(ℎ ∘ 𝑔 ∘ 𝑓)(1)

= h (g (f (1)))

= h (g (5))

= h (16) 

ℎ(𝑥) = 2𝑥 + 3

h(16) = 2(16) + 3

h(16) = 32 + 3

h(16) = 35

Jawaban : C