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Jika f(x) = x² +2 dan g(x)=1/x-1Tentukan (gof)(x) dan (fog)(x)

jika f(x) = x² +2 dan g(x)=1/x-1Tentukan (gof)(x) dan (fog)(x)

Jawaban:
(g o f)(x) = 1/(x²+1)
(f o g)(x) = (2x² – 4x + 3)/(x² – 2x + 1)

perhatikan konsep fungsi komposisi berikut:
(g o f)(x) = g(f(x))
(f o g)(x) = f(g(x))

Diketahui:
f(x) = x²+2
g(x) = 1/(x-1)

Ditanya:
(g o f)(x) = …
(f o g)(x) = …

Pembahasan:
(g o f)(x) = g(f(x))
(g o f)(x) = 1/(f(x) – 1)
(g o f)(x) = 1/(x²+2 – 1)
(g o f)(x) = 1/(x²+1)

(f o g)(x) = f(g(x))
(f o g)(x) = (f(x))²+2
(f o g)(x) = (1/(x-1))²+2
(f o g)(x) = ((1)(1))/((x-1)(x-1)) + 2
(f o g)(x) = (1)/(x² – 2x + 1) + 2
(f o g)(x) = (1)/(x² – 2x + 1) + 2(x² – 2x + 1)/(x² – 2x + 1)
(f o g)(x) = (1)/(x² – 2x + 1) + (2x² – 4x + 2)/(x² – 2x + 1)
(f o g)(x) = (1 + 2x² – 4x + 2)/(x² – 2x + 1)
(f o g)(x) = (2x² – 4x + 3)/(x² – 2x + 1)
(f o g)(x) = (2x² – 4x + 3)/(x² – 2x + 1)

Kesimpulan jawaban:
(g o f)(x) = 1/(x²+1)
(f o g)(x) = (2x² – 4x + 3)/(x² – 2x + 1)

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