Question

If $f:R-\left\{\frac{3}{5}\right\}\to R-\left\{\frac{3}{5}\right\};f\left(x\right)=\frac{3x+1}{5x-3}$, then ___________.

• A. $f^{-1}\left(x\right)=2f\left(x\right)$
• B. $f^{-1}\left(x\right)=f\left(x\right)$
• C. $f^{-1}\left(x\right)=-f\left(x\right)$
• D. $f^{-1}\left(x\right)$ does not exists

Answer 1

Answer: (B)

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

$f\left(x\right)=\frac{3x+1}{5x-3}$ .... $\left(i\right)$
We know that if $f\left(x\right)=\frac{ax+b}{cx+d}$ and $a+d=0$, then
$f\left(x\right)=f^{-1}\left(x\right)$

From $\left(i\right)$, we get

$a=3,b=1,c=5,d=-3$

$a+d=3-3=0$

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