已知f(x)=1/(1+4的0.5-x次方)

来源：百度知道 编辑：UC知道 时间：2024/05/18 04:13:59
1.化简f(x)
2.求f(1-x),并探究f(x)与f(1-x)的关系
3.求f(1/1001)+f(2/1001)+f(3/1001)……+f(1000/1001)的值
要过程

f(x)=1/[1+4^(0.5-x)]
=1/[1+4^0.5/4^x]
=1/(1+2/4^x)
=4^x/(4^x+2)

f(1-x)=4^(1-x)/[4^(1-x)+2]
=(4/4^x)/[(4/4^x)+2]
=4/(4+2*4^x)
=2/(2+4^x)
f(x)=4^x/(4^x+2)
所以f(x)+f(1-x)=(4^x+2)/(4^x+2)=1

f(1/1001)+f(2/1001)+f(3/1001)……+f(1000/1001)
=[f(1/1001)+f(1000/1001)]+[f(2/1001)+f(999/1001)]+……+[f(500/1001)+f(501/1001)]
=[f(1/1001)+f(1-1/1001)]+[f(2/1001)+f(1-2/1001)]+……+[f(500/1001)+f(1-500/1001)]
=1+1+……+1
=500*1
=500