invers dari (fog) (x) dan (gof) (x) dari f(x)=5-1 dan g(x)=8x-2
Matematika
rdapubeang
Pertanyaan
invers dari (fog) (x) dan (gof) (x) dari f(x)=5-1 dan g(x)=8x-2
1 Jawaban
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1. Jawaban whongaliem
f (x) = 5x - 1 dan g (x) = 8x - 2
f (x) = 5x - 1
y = 5x - 1
5x = y - 1
x = (1/5)y - 1/5
f^-1 (x) = (1/5)x - 1/5)
g (x) = 8x - 2
y = 8x - 2
8x = y + 2
x = (1/8)y + 2/8
g ^-1(x) = (1/8)x + 2/8
g^-1 (x) = (1/8)x + 1/4
a) (f o g)^-1(x) = g^-1 (f^-1 (x))
= g^-1 (1/5 x - 1/5)
= 1/8 (1/5 x - 1/5) + 1/4
= (1/40) x - (1/40) + 10 /40
= (1/40) x + 9 / 40)
= (1/40) (x + 9)
b) (g o f)^-1 (x) = f^-1 (g^-1 (x))
= f^-1 ( 1/8 x + 1/4)
= 1/5 (1/8 x + 1/4) - 1/5
= (1/40) x + 1/20 - 1/5
= (1/40) x + 2 / 40 - 8 / 40
= (1/40) x - 6 / 40
= (1/40) ( x - 6)