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Find the function f(x)that satisfy the given Relationf(x) + f(1/(1-x)) = 2(1-2x) / x(1-x)

Find the function f(x)that satisfy the given Relationf(x) + f(1/(1-x)) = 2(1-2x) / x(1-x)

Grade:12th pass

1 Answers

rajusharma
12 Points
10 years ago
f(x)+f(1/(1-x))=2(1-2x)/x(1-x)=2{(1+x^2-2x)-x^2}/x(1-x)=2{(1-x)^2-x^2}/x(1-x)=2(1-x)/x - 2x/(1-x) f(x)+f(1/(1-x)) = 2/x-2-2/(1/x-1)={-1+2/x}+{-1+2/(1-1/x)} hence f(x)=-1+2/(1-1/x)

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