If $$\mathrm{f}(x)=\frac{2 x-3}{3 x-4}, x \neq \frac{4}{3}$$, then the value of $$\mathrm{f}^{-1}(x)$$ is

If $$\mathrm{f}^{\prime}(x)=\sin (\log x)$$ and $$y=\mathrm{f}\left(\frac{2 x+3}{3-2 x}\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=1$$ is

The area bounded by the curve $$y=|x-2|, x=1, x=3$$ and $$X$$-axis is

$$\int \frac{\mathrm{d} x}{\cot ^2 x-1}=\frac{1}{\mathrm{~A}} \log |\sec 2 x+\tan 2 x|-\frac{x}{\mathrm{~B}}+\mathrm{c}$$, (where $$\mathrm{c}$$ is constant of integration), then $$\mathrm{A}+\mathrm{B}=$$