函数y=2^x+1/2^x-1 (x<0) 的反函数?定义域？

反函数定义域为函数的值域
y=2^x+1/2^x-1 =1+2/(2^x-1)
x<0 => 0<2^x<1 => -1<2^x-1<0 => 1 /(2^x-1)<-1
=>1+2/(2^x-1)<1+2*(-1)=-1
故反函数定义域为x<-1
y=2^x+1/2^x-1
=> (y-1)2^x=y+1 =>2^x=(y+1)/(y-1)
=>x=log(下2)[(y+1)/(y-1)]
=>反函数y=log(下2)[(x+1)/(x-1)] (x<-1)

教你一种方法,把原函数化成用Y来表示X,再把X改成Y,Y改成X,求到反函数为Y=log2(x+1/x-1),解得x<-1或x>1