Question

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

• A. $f^{-1}\left(x\right)=fx$
• 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

Answer: (A), (C)

The correct options are
A $f^{-1}\left(x\right)=fx$
C $fof\left(x\right)=-x$

Given that $f\left(x\right)=\frac{3x+2}{5x-3}$.

Let $y=\frac{3x+2}{5x-3}$.

$3x+2=5xy-3y\Rightarrow x(3-5y)=-3y-2$

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

$f^{-1}\left(x\right)=f\left(x\right)$