Question:
If $y=f(x)=\frac{a x-b}{b x-a}$, show that $x=f(y)$.
Solution:
Given:
$f(x)=\frac{a x-b}{b x-a}$
Let y = f (x) .
⇒ y( bx
⇒ xyb – ay = ax – b
⇒ xyb – ax = ay – b
⇒ x(by – a) = ay – b
$\Rightarrow x=\frac{a y-b}{b y-a}$
⇒ x = f (y)
Hence proved.
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