At first, I tried solving the functional equation in general without success. But asking only for f(0) rather than for f(x) is a much smaller problem.
If f(0)=0 --> f(0)=0^2 - 0 + 1 = 1, an inconsistency.
If f(0)=1 --> f(1)=1^2 - 1 + 1 = 1, consistent
If f(0)=k --> f(k)=k^2 - k + 1= k to be consistent, or
k^2 - 2k + 1 = 0
(k-1)^2 = 0
So k = f(0) = 1 is the only solution
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Posted by Larry
on 2023-04-14 12:37:30 |
Solution
