f(x),定义域x≠1(x∈R),满足f(1∕1-x)=【1∕2f(x)】+1,求f(3)
f(x),定义域x≠1(x∈R),满足f(1∕1-x)=【1∕2f(x)】+1,求f(3)
数学人气:156 ℃时间:2020-02-05 19:33:15
优质解答
令1/(1-x)=3x=2/3则f(3)=1/2*f(2/3)+1令1/(1-x)=2/3x=-1/2则f(2/3)=1/2*f(-1/2)+1所以f(3)=1/2*[1/2*f(-1/2)+1]+1=1/4*f(-1/2)+3/21/(1-x)=-1/2x=3则f(-1/2)=1/2*f(3)+1代入f(3)=1/4*f(-1/2)+3/2所以f(3)=1/4*[1/2*f...
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