f-x-f-x-f-x-

Question Number 4817 by 123456 last updated on 15/Mar/16

f (α x) = α f (x - α)

f (x) = ?

Commented by prakash jain last updated on 15/Mar/16

x = 0

Trivial solution satisfies the equation f (x) = 0

f (x) = a x + b

f (α x) = a α x + b

α f (x - α) = α a x - a α^{2} + α b

α b - a α^{2} = b

b = \frac{a α^{2}}{α - 1}

f (x) = a x + \frac{a α^{2}}{α - 1}