g(x) = x + 3 dan (g o f)(x) = x²+6x-4 , maka f-¹ (x)
Matematika
alanalann
Pertanyaan
g(x) = x + 3 dan (g o f)(x) = x²+6x-4 , maka f-¹ (x)
1 Jawaban
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1. Jawaban arsetpopeye
(g o f)(x) = x² + 6x - 4
g(f(x)) = x² + 6x - 4
f(x) + 3 = x² + 6x - 4
f(x) = x² + 6x - 7
x² + 6x - 7 = y
x² + 6x + ... = y + 7 + ....
x² + 6x + 9 = y + 7 + 9
(x + 3)² = y + 16
x + 3 = ± √(y + 16)
x = - 3 ± √(y + 16)
f^-1(x) = -3 ± √(x + 16)
f^-1(x) = -3 + √(x + 16) atau f^-1(x) = -3 + √(x + 16)