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

Answer:

Consider,

y = (ax – b) / (bx – a)

[Cross multiply]

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, showed.