已知函数f(x)=4^x/(4^x+2) (1)求f(a)+f(1-a)的值 (2)求f(1/100)+f(2/100)+f(3/100)+……+f(99/100)
问题描述:
已知函数f(x)=4^x/(4^x+2) (1)求f(a)+f(1-a)的值 (2)求f(1/100)+f(2/100)+f(3/100)+……+f(99/100)
答
f(x)=4^x/(4^x+2)=1-2/(4^x+2)f(a)+f(1-a)=1-2/(4^a+2)+1-2/(4^(1-a)+2)=2-2[1/(4^a+2)+1/(4/4^a+2)]=2-2[1/(4^a+2)+4^a/(2*4^a+4)]=2-2[1/(4^a+2)+1/2*4^a/(4^a+2)]=2-2(1+1/2*4^a)/(4^a+2)=1f(1/100)+f(2/...