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

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in Differential equations by (63.5k points)

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

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

⇒ (bx – a) y = ax – b 

⇒ bx y – ay = ax – b 

⇒ x (by – a) = ay – b

⇒ x = (ax - b)/(bx - a)

⇒ x = f(y)

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