3

Part of 2022 Peru MO (ONEM)

Problems(1)

f(xy) + y + f(x + f(y)) = (y + 1)f(x)

Source: 2022 Peru MO (ONEM) L3 p3 - finals

R

be the set of real numbers and

f : R \to R

be a function that satisfies:

f(xy) + y + f(x + f(y)) = (y + 1)f(x),

for all real numbers

x, y

. a) Determine the value of

f(0)

. b) Prove that

f(x) = 2-x

for every real number

x

algebrafunctional equationfunctional