Mohon bantuannya nomor 3 dan 4. Terima kasih
Matematika
ameltw
Pertanyaan
Mohon bantuannya nomor 3 dan 4. Terima kasih
1 Jawaban
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1. Jawaban arsetpopeye
3) f(x) - 2f(1 - x) = x^2 ..... (1)
Jika x nya diganti dengan 1 - x maka diperoleh
f(1 - x) - 2f(1 - (1 - x)) = (1 - x)^2
f(1 - x) - 2f(1 - 1 + x) = 1 - 2x + x^2
f(1 - x) - 2f(x) = 1 - 2x + x^2 ---------> kali 2
2f(1 - x) - 4f(x) = 2 - 4x + 2x^2 ....... (2)
Eliminasi 1 dan 2
f(x) - 2f(1 - x) = x^2
2f(1 - x) - 4f(x) = 2 - 4x + 2x^2
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-3 f(x) = 2 - 4x + 3x^2
f(x) = (2 - 4x + 3x^2)/(-3)
f(x) = (-3x^2 + 4x - 2)/3
f(x) = -x^2 + 4/3 x - 2/3
4) f(2x + 4) = x
Misal 2x + 4 = a => 2x = a - 4 => x = (a - 4)/2
f(a) = (a - 4)/2
f(2) = (2 - 4)/2 = (-2)/2 = -1
g(3 - x) = x
Misal a = 3 - x => x = 3 - a
g(a) = 3 - a
g(1) = 3 - 1 = 2
g(-1) = 3 - (-1) = 4
f(g(1)) - g(f(2)) = f(2) - g(-1) = -1 - 4 = -5