Diketahui:
g(x) = (1-x)²
(fog)(x) = (x²-2x)²
Ditanyakan:
f(3/4)
Jawab:
(fog)(x) = f(g(x))
(x²-2x)² = f((1-x)²)
misal (1-x)² = a
maka
(1-x)² = a
1-x = √a
1-√a = x
f(a) = ((1-√a)²-2(1-√a))²
= (1-2√a+a-2+2√a)²
= (a-1)²
f(x) = (x-1)²
f(3/4) = ((3/4)-1)²
= ((3/4)-(4/4))²
= (-1/4)²
= 1/16
Mapel: Matematika
Kelas: 10
Materi: Komposisi Fungsi
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Diketahui:
g(x) = (1-x)²
(fog)(x) = (x²-2x)²
Ditanyakan:
f(3/4)
Jawab:
(fog)(x) = f(g(x))
(x²-2x)² = f((1-x)²)
misal (1-x)² = a
maka
(1-x)² = a
1-x = √a
1-√a = x
f(a) = ((1-√a)²-2(1-√a))²
= (1-2√a+a-2+2√a)²
= (a-1)²
f(x) = (x-1)²
f(3/4) = ((3/4)-1)²
= ((3/4)-(4/4))²
= (-1/4)²
= 1/16
Mapel: Matematika
Kelas: 10
Materi: Komposisi Fungsi