Question

If $f:(-\infty ,\infty )\to (-\infty ,\infty )$ is defined by $f\left(x\right)=5x-6$, then $f^{-1}\left(x\right)=$

• A. $\frac{x+5}{6}$
• B. $\frac{x-5}{6}$
• C. $\frac{x-6}{5}$
• D. $\frac{x+6}{5}$

Answer 1

The correct option is D $\frac{x+6}{5}$

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