diketahui f(x)=1/x+1 dan g(x)=x+1/x ,maka (fog)-¹(2/5)
Matematika
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Pertanyaan
diketahui f(x)=1/x+1 dan g(x)=x+1/x ,maka (fog)-¹(2/5)
1 Jawaban
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1. Jawaban sulthanbahmid
f(x) = 1/(x + 1)
g(x) = (x + 1)/x
(f • g)(x) = 1/((x + 1)/x + 1)
(f • g)(x) = 1/((x + 1)/x + x/x)
(f • g)(x) = 1/((2x + 1)/x)
(f • g)(x) = x/(2x + 1)
(f • g)(x) = y
x/(2x + 1) = y
x = y(2x + 1)
x = 2xy + y
x - 2xy = y
x(1 - 2y) = y
x = y/(1 - 2y)
(f • g)(x)^-1 = x/(1 - 2x)