Kisi Kisi PAT Matematika Kelas XI no 27

27. Diberikan 𝑓(𝑥) = 𝑥^2 + 2 dan 𝑔(𝑥) = 𝑥^2 − 2. Hasil dari (𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥)= ...

a. 8𝑥^2 + 4

b. 8𝑥^2 − 4

c. −8𝑥^2 + 4

d. 4

e. −4

Jawaban :

𝑓(𝑥) = 𝑥^2 + 2

𝑔(𝑥) = 𝑥^2 − 2

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = g (f (x)) - f (g(x))

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = g (𝑥^2 + 2) - f (𝑥^2 − 2)

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = (𝑥^2 + 2)^2 − 2 - ((𝑥^2 − 2)^2 + 2)

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = (𝑥^4 + 4x^2 + 4)− 2 - ((𝑥^4 − 4x^2 + 4) + 2)

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = 𝑥^4 + 4x^2 + 4 − 2 - 𝑥^4 + 4x^2 - 4 - 2

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = 𝑥^4 + 4x^2 + 2 - 𝑥^4 + 4x^2 - 6

(𝑔 𝑜 𝑓)(𝑥) − (𝑓 𝑜 𝑔)(𝑥) = 8x^2 - 4

Jawaban : B