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Question Number 165848 by leonhard77 last updated on 09/Feb/22
f((1/x))+f(1−x)=x f(x)=?
f(1x)+f(1−x)=xf(x)=?
Answered by qaz last updated on 10/Feb/22
f(x)+f(1−(1/x))=(1/x) ⇒f(x)=(1/x)−f(1−(1/x)) =(1/x)−[(1/(1−(1/x)))−f(1−(1/(1−(1/x))))] =(1/x)−(x/(x−1))+f((1/(1−x))) =(1/x)−(x/(x−1))+1−x−f(x) ⇒f(x)=(1/2)((1/x)−(x/(x−1))+1−x)
f(x)+f(1−1x)=1x⇒f(x)=1x−f(1−1x)=1x−[11−1x−f(1−11−1x)]=1x−xx−1+f(11−x)=1x−xx−1+1−x−f(x)⇒f(x)=12(1x−xx−1+1−x)

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