谁会这道题 40
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将(x-1)/x代入x得
f((x-1)/x)+f(((x-1)/x -1)/(x-1)/x)=1+(x-1)/x
f((x-1)/x)+f(-1/(x-1))=1+(x-1)/x
f((x-1)/x)+f(1/(1-x))=2 - 1/x
所以f(x)-f(1/(1-x))=x+1/x-1 ②
将1/(1-x)代入x得
f(1/(1-x))+f(1-(1-x))=1+1/(1-x)
f(1/(1-x))+f(x)=1+1/(1-x)③
②+③得2f(x)=x+1/x+1/(1-x)从而得f(x)
f((x-1)/x)+f(((x-1)/x -1)/(x-1)/x)=1+(x-1)/x
f((x-1)/x)+f(-1/(x-1))=1+(x-1)/x
f((x-1)/x)+f(1/(1-x))=2 - 1/x
所以f(x)-f(1/(1-x))=x+1/x-1 ②
将1/(1-x)代入x得
f(1/(1-x))+f(1-(1-x))=1+1/(1-x)
f(1/(1-x))+f(x)=1+1/(1-x)③
②+③得2f(x)=x+1/x+1/(1-x)从而得f(x)
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