diketahui f(x) = x^2 -5 dan g(x+1)=2x+1/x-6 ;x#6.rumus komposisi fungsi (gof)(x)

Mapel : Matematika

Kelas : 10

Bab : Fungsi Komposisi
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f(x) = x² - 5

g(x + 1) = 2x + 1/x - 6

Ditanya → (g o f) (x) =...?

Jawaban :
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Misalkan,

x + 1 = y
x = y - 1

Maka, fungsi g(x)

g(x) = [2(x - 1) + 1]/[(x - 1) - 6]

g(x) = 2x - 2 + 1/x - 7

g(x) = 2x - 1/x - 7


Maka, fungsi komposisi (g o f) (x)

(g o f) (x) = g(x² - 5)

(g o f) (x) = 2(x² - 5) - 1/(x² - 5) - 7


(g o f) (x) = (2x² - 11) / (x² - 12)