Question

Let $f:R-\left(\frac{3}{5}\right\}\to R-\left(\frac{3}{5}\right\}bedefinedbyf\left(x\right)=\frac{3x+2}{5x-3}.$
Then

• A. $f^{-1}\left(x\right)=f\left(x\right)$
• B. $f^{-1}\left(x\right)=-f\left(x\right)$
• C. $fof\left(x\right)=-x$
• D. $f^{-1}\left(x\right)=\frac{1}{19}f\left(x\right)$

Answer 1

The correct option is A $f^{-1}\left(x\right)=f\left(x\right)$

$\mathrm{Let}y=f\left(x\right)y=\frac{3x+2}{5x-3}\Rightarrow 5\mathrm{xy}-3y=3x+2\Rightarrow 5\mathrm{xy}-3x=3y+2\Rightarrow x\left(5y-3\right)=3y+2\Rightarrow x=\frac{3y+2}{5y-3}\Rightarrow f^{-1}\left(y\right)=\frac{3y+2}{5y-3}[y=f(x)\Rightarrow x=f^{-1}(y\left)\right]\Rightarrow f^{-1}\left(x\right)=\frac{3x+2}{5x-3}=f\left(x\right)$