38th Putnam 1977

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Problem A3

R is the reals. f, g, h are functions R → R. f(x) = (h(x + 1) + h(x - 1) )/2, g(x) = (h(x + 4) + h(x - 4) )/2. Express h(x) in terms of f and g.

 

Solution

Easy

h(x) = g(x) - f(x - 3) + f(x - 1) + f(x + 1) - f(x + 3).

Other expressions are also true.

 


 

38th Putnam 1977

© John Scholes
jscholes@kalva.demon.co.uk
30 Nov 1999