tolong dibantu segera
Matematika
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Pertanyaan
tolong dibantu segera
1 Jawaban
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1. Jawaban arsetpopeye
(g o f)(x) = 4x^2 + 6x - 4
g(f(x)) = 4x^2 + 6x - 4
g(2x + 4) = 4x^2 + 6x - 4
Misal (2x + 4) = a => 2x = (a - 4) => x = (a - 4)/2
g(a) = 4((a - 4)/2)^2 + 6(a - 4)/2 - 4
g(a) = 4 (a^2 - 8a + 16)/4 + 3(a - 4) - 4
g(a) = a^2 - 8a + 16 + 3a - 12 - 4
g(a) = a^2 - 5a
g(x) = x^2 - 5x
x^2 - 5x = y ===> kedua ruas ditambah 25/4
x^2 - 5x + 25/4 = y + 25/4
(x - 5/2)^2 = (4y + 25)/4
(x - 5/2) = ±√((4y + 25)/4)
x = 5/2 ± √(4y + 25) / 2
x = (5 ± √(4y + 25)) / 2
g^-1(x) = (5 ± √(4x + 25)) / 2