已知函数y=f(x)=2的x次方减一除以2的x次方加一的值域是

Question

已知函数y=f(x)=2的x次方减一除以2的x次方加一 的值域是

Answer 1

f(x)=(2^x-1)/(2^x+1)
y=(2^x-1)/(2^x+1)
2^x-1=y2^x+y
(1-y)2^x=(y+1)
2^x=(y+1)/(1-y)>0
(y+1)/(y-1)<0
-1所以原函数的值域为：(-1,1)