Question

If $y=f\left(x\right)=\frac{ax-b}{bx-a}$, show that $x=f\left(y\right)$.

Answer 1

We have,
$y=f\left(x\right)=\frac{ax-b}{bx-a}$
$\Rightarrow y=\frac{ax-b}{bx-a}$
$\Rightarrow y(bx-a)=ax-b$
$\Rightarrow xyb-ay=ax-b$
$\Rightarrow xyb-ax=ay-b$
$\Rightarrow x(by-a)=ay-b$
$\Rightarrow x=\frac{ay-b}{by-a}$
$\Rightarrow x=f\left(y\right)$