Question

If $y=f\left(x\right)=\frac{x-5}{5x-1}$, show that $f\left(y\right)=x$.

Answer 1

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