jika f(x) = 1/2x-1 dan (fog)(x) = x/3x-2 maka nilai g(1) adalah

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

[tex]\displaystyle (f\circ g)(x)=\frac{x}{3x-2}\\f(g(x))=\frac{x}{3x-2}\\\frac{1}{2g(x)-1}=\frac{x}{3x-2}\\\frac{3x-2}{x}=2g(x)-1\\\frac{3x-2}{x}+1=2g(x)\\\frac{2x-1}{x}=g(x)\\\\\frac{2(1)-1}{1}=g(1)\\\frac{2-1}{1}=g(1)\\\boxed{\boxed{g(1)=1}}[/tex]