Question

If $f\left(x\right)=\frac{5x+6}{7x+9}$ then $f^{-1}\left(x\right)=$

• A. $\frac{y+6}{7y+9}$
• B. $\frac{7y+9}{5y+6}$
• C. $\frac{9y-6}{-7y+9}$
• D. $\frac{9y-6}{-7y+5}$

Answer 1

Answer: (D)

$\frac{9y-6}{-7y+5}$

Let $f\left(x\right)=y=\frac{5x+6}{7x+9}$
$7xy+9y=5x+6$
$\Rightarrow x(7y-5)=6-9y$
$x=\frac{9y-6}{-7y+5}$
$x=f^{-1}\left(y\right)=\frac{9y-6}{-7y+5}$