Diketahui (f o g) (x) = x - 1 / x + 2 dan g(x) = 1 / x - 2. Tentukan f(x)

Diketahui (f o g) (x) = x – 1 / x + 2 dan g(x) = 1 / x – 2. Tentukan f(x)

Rumus fungsi f(x) adalah 1/(1 + 3x).

Diketahui:

(f o g)(x) = (x – 1)/(x + 2)

g(x) = 1/(x – 2)

Ditanya:

f(x) = …

Penyelesaian:

Misalkan,

g(x) = a

1/(x – 1) = a

a(x – 1) = 1

x – 1 = 1/a

x = 1/a + 1

(f o g)(x) = (x – 1)/(x + 2)

f( g(x) ) = (x – 1)/(x + 2)

f(a) = (1/a + 1 – 1)/(1/a + 1 + 2)

f(a) = (1/a)/(1/a + 3)

f(a) = (1/a)/(1/a + 3a/a)

f(a) = (1/a)/((1 + 3a)/a)

f(a) = 1/a x a/(1 + 3a)

f(a) = 1/(1 + 3a)

f(x) = 1/(1 + 3x)

Jadi rumus fungsi f(x) = 1/(1 + 3x).

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