1.

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

Answer»

Given,

y = f(x) = (ax-b)/(bx-a)

⇒ f(y) = \(\frac{ay-b}{by-a}\) 

We need to prove that x = f(y).

We have,

y = \(\frac{ax-b}{bx-a}\)

⇒ y(bx – a) = ax – b 

⇒ bxy – ay = ax – b 

⇒ bxy – ax = ay – b 

⇒ x(by – a) = ay – b

⇒ x = \(\frac{ay-b}{by-a}\) = f(y)

∴ x = f(y) 

Thus, 

x = f(y).


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