Question

Terimakasih bagi yang membantuuu :)


Tentang komposisi dan Invers


g(x+1)= (2x-7) per(3x+7)
Nilai x yang memenuhi (g o g)^-1(x)= 3x+4 adalah

Answer 1

G(x+1)=(2x-7)/(3x+7)
Jadi nilai g(x)=(2x+5)/(3x+4)

lalu cari nilai g^-1(x)
g(x)=y
y=(2x+5)/(3x+4)
y(3x+4)=2x+5
3xy+4y=2x+5
3xy-2x=5-4y
x(3y-2)=5-4y
x=(5-4y)/(3y-2)
jadi g^-1(x)=(5-4x)/(3x-2)

ditanya g^-1(g(x))
g^-1(g(x))=(5-4((2x+5)/(3x+4)) / (3((2x+5)/(3x+4))-2)
g^-1(g(x))=(5-(8x+20)/(3x+4)) / ((6x+15)/(3x+4)-2)
g^-1(g(x))=((15x+20)-(8x+20))/(3x+4)) / ((6x+15)-(6x+8)/(3x+4)) --> 
g^-1(g(x))=7x/(3x+4) / 7/(3x+4)
g^-1(g(x))=(7x/(3x+4)) x ((3x+4)/7)
g^-1(g(x))= x

Answer 2

G(x+1)  = (2x-7)/(3x+7)

misal x+1 = a
x = a - 1
.
g(a) = { 2(a-1) -7} / {3(a-1) + 7}
g(a) = (2a-2-7)/(3a-3+7)
g(a)= (2a -9)/(3a +4)
g(x)= (2x- 9)/(3x + 4)