Question

1)diketahui g(x)= dan (fog)(x)=2x+3 . maka tentukan nilai f(x)
2)diketahui f(x)= dan (gof)(x)= . maka tentukan g(x)
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Answer 1

(fog)(x)=2x+3
f(g(x))=2x+3
f((x+2)/x)=2x+3

misalkan (x+2)/x=p
maka x+2=px
2=px-x
2=x(p-1)
x=2/(p-1)

f(p)=2(2/(p-1))+3
f(p)=4/(p-1)+3
f(p)=(4+3p-3)/(p-1)
f(p)=(3p+1)/(p-1)
f(x)=(3x+1)/(x-1)


no.2
(gof)(x)=6x^2 +9x +7
g(f(x))=6x^2 +9x +7
g(2x^2+3x-1) = 6x^2 +9x +7
g(2x^2+3x-1) = 6x^2 +9x -3+10
g(2x^2+3x-1) = 3(2x^2+3x-1)+10
g(p) = 3p+10
g(x)=3x+10