Question

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

Answer 1

Given:
$f\left(x\right)=\frac{ax-b}{bx-a}$
Let y = f (x) .
⇒ y( bx $-$ a) = ax – b
⇒ xyb – ay = ax – b
⇒ xyb – ax = ay – b
⇒ x(by – a) = ay – b
$\Rightarrow x=\frac{ay-b}{by-a}$
⇒ x = f (y)
Hence proved.