Question

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

Answer 1

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.