jika(f)=1/2x-1 dan g(x)=2x+4, maka tentukan (g o f)-1(10)
Matematika
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Pertanyaan
jika(f)=1/2x-1 dan g(x)=2x+4, maka tentukan (g o f)-1(10)
1 Jawaban
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1. Jawaban bapakdr
f(x) = 1/2x - 1
gof(x) = 2(1/2x - 1) + 4
= 1/x - 2 + 4
= 1/x + 2
= 1/x + 2x/x
= (1 + 2x)/x
gof(x) = (2x + 1)/x
y = (2x + 1)/x
yx = 2x + 1
yx - 2x = 1
x(y - 2) = 1
x = 1 / (y - 2)
(gof)-¹(x) = 1 / (x - 2)
(gof)-¹(10) = 1 / (10-2)
= 1/8