f(x)= (3x-2)/(2x+3) g(x)= 2x-1 maka (fog)^-1 adalah

[tex]
\left(f\circ g\right)(x)\\
=f\left(g(x)\right)\\
=f\left(2x-1\right)\\
=\frac{3(2x-1)-2}{2(2x-1)+3}\\
=\frac{6x-7}{4x+1}\\
\text{Misalkan }y=(f\circ g)(x)\text{, selanjutnya}\\
y=\frac{6x-7}{4x+1}\\
\Leftrightarrow 4xy+y=6x-7\\
\Leftrightarrow 4xy-6x=-y-7\\
\Leftrightarrow x(4y-6)=-(y+7)\\
\Leftrightarrow x=-\frac{y+7}{4y-6}\\
\Leftrightarrow \left(f\circ g\right)^{-1}(y)=-\frac{y+7}{4y-6}\\
\Leftrightarrow \left(f\circ g\right)^{-1}(x)=-\frac{x+7}{4x-6}
[/tex]