已知函数f(x)=9^x/(9^x+3),求f(1/11)+f(2/11)+……+f(10/11)
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已知函数f(x)=9^x/(9^x+3),求f(1/11)+f(2/11)+……+f(10/11)
已知函数f(x)=9^x/(9^x+3),求f(1/11)+f(2/11)+……+f(10/11)
已知函数f(x)=9^x/(9^x+3),求f(1/11)+f(2/11)+……+f(10/11)
因为f(x)=9^x/(9^x+3),所以f(1-x)=9^(1-x)/[9^(1-x)+3],
f(x)+f(1-x)=9^x/(9^x+3)+9^(1-x)/[9^(1-x)+3]=9^x/(9^x+3)+9/(9+3*9^x)
=9^x/(9^x+3)+3/(3+9^x)=1,
所以f(1/11)+f(2/11)+……+f(10/11)=[f(1/11)+f(10/11)]+[f(2/11)+f(9/11)]+...+[f(5/11)+f(6/11)]
=1+1+1+1+1=5
f(x)=9^x/(9^x+3)=1-3/(9^x+3)
设x1+x2=1,则f(x1)+f(x2)=2-1=1
f(1/11)+f(2/11)+……+f(10/11)=5