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Question

If f(x)=log1x1+x then f(a)+f(b)=

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Solution

f(x)=log1x1+xf(a)+f(b)=log1a1+a+log1b1+bwecanusethatlogx+logy=logxyandlogxlogy=logxy.Thenf(a)+f(b)=log(1a)(1b)log(1+a)(1+b).alternativelyf(a)+f(b)=log(1a)(1b)(1+a)(1+b).

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