3

Part of 1968 German National Olympiad

Problems(1)

a f(x^n) + f(-x^n) = b

Source: 1967-68 Germany R4 12.3

Specify all functions

y = f(x)

, each in the largest possible domain (within the range of real numbers) of the equation

a \cdot f(x^n) + f(-x^n) = bx

b

is any real number,

n

is any odd natural number and

a

is a real number with

|a| \ne 1

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