Question

$f\left(x\right)=y=\frac{ax-b}{cx-a}$ then prove that $f\left(y\right)=x$

Answer 1

$f\left(x\right)=y=\frac{ax-b}{cx-a}$

Express $x$ in terms of $y$

$y(cx-a)=ax-b$

$cxy-ay=ax-b$

$cxy-ax=ay-b$

$x(cy-a)=ay-b$

$x=\frac{ay-b}{cy-a}=f\left(y\right)$