littlemathquark
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- TL;DR Summary
- Let ##f## be defined over positive reals. ##f(2x)=f^2(x)-2f(x)-1/2## and ##f(1)=2## then find ##f(3)##
My solution:
Let ##f(x+y)=f(x)f(y)-[f(x)+f(y)]-1/2##
İf ##y=x## we find functional equation that given us. So for ##x=y=1## then ##f(2)=-1/2##
İf we evaluate ##x=1, y=2## at above equation ##f(3)=-3##
My question is: What is the solution of that functional equation; I mean are there other solutions? İf so it must be other values of ##f(3)##
Let ##f(x+y)=f(x)f(y)-[f(x)+f(y)]-1/2##
İf ##y=x## we find functional equation that given us. So for ##x=y=1## then ##f(2)=-1/2##
İf we evaluate ##x=1, y=2## at above equation ##f(3)=-3##
My question is: What is the solution of that functional equation; I mean are there other solutions? İf so it must be other values of ##f(3)##