If y = f (x) = (ax – b) / (bx – a), show that x = f (y).

1.	If y = f (x) = (ax – b) / (bx – a), show that x = f (y).
Answer» Given as y = f (x) = (ax – b) / (bx – a) ⇒ f (y) = (ay – b) / (by – a) Let us prove that the x = f (y). Now, we have, y = (ax – b) / (bx – a) On cross-multiplying, y(bx – a) = ax – b bxy – ay = ax – b bxy – ax = ay – b x(by – a) = ay – b x = (ay – b) / (by – a) = f (y) ∴ x = f (y) Thus proved.

Answer»

Given as

y = f (x) = (ax – b) / (bx – a) ⇒ f (y) = (ay – b) / (by – a)

Let us prove that the x = f (y).

Now, we have,

y = (ax – b) / (bx – a)

On cross-multiplying,

y(bx – a) = ax – b

bxy – ay = ax – b

bxy – ax = ay – b

x(by – a) = ay – b

x = (ay – b) / (by – a) = f (y)

∴ x = f (y)

Thus proved.

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