Diketahui f(x) =2x-1 / x+1, g (x) =x^2-1, dan h(x) =3x+5 Tentukan: (h^-1 o f^-1)(x)
Matematika
benedict15
Pertanyaan
Diketahui f(x) =2x-1 / x+1, g (x) =x^2-1, dan h(x) =3x+5
Tentukan:
(h^-1 o f^-1)(x)
Tentukan:
(h^-1 o f^-1)(x)
1 Jawaban
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1. Jawaban riskiapis50456ou9aji
FungSI KompoSISI
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f (x) = (2x - 1)/(x + 1)
y = (2x - 1)/(x + 1)
xy + y = 2x - 1
xy - 2x = -1 - y
x (y - 2) = -1 - y
x = (-1 -y)/(y - 2)
f^-1 (x) = (-1 - x)/(x - 2)
h (x) = 3x + 5
y = 3x + 5
y - 5 = 3x
(y - 5)/3 = x
(x - 5)/3 = h^-1 (x)
(f^-1 o h^-1) (x) = f^-1(h^-1) (x)
= (-1 - ((x - 5)/3))/((x -5)/3) - 2)
= (-3x + 6)/(3x - 33)
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