Home Competitions NL-NWO 1965 Problem 5
The function ƒ. which is defined for all real numbers satisfies: f ( x + y ) + f ( x − y ) = 2 f ( x ) + 2 f ( y ) f(x+y)+f(x-y)=2f(x)+2f(y) f ( x + y ) + f ( x − y ) = 2 f ( x ) + 2 f ( y ) f ( 0 ) = 0 f(0) = 0 f ( 0 ) = 0 f ( − x ) = f ( x ) f(-x) = f(x) f ( − x ) = f ( x ) f ( 2 x ) = 4 f ( x ) f(2x) = 4 f (x) f ( 2 x ) = 4 f ( x ) f ( x + y + z ) = f ( x + y ) + f ( y + z ) + f ( z + x ) − f ( x ) − f ( y ) − f ( z ) . f(x + y + z) = f(x + y) + f(y + z) + f(z + x) -f(x) - f(y) -f(z). f ( x + y + z ) = f ( x + y ) + f ( y + z ) + f ( z + x ) − f ( x ) − f ( y ) − f ( z ) .
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