Question

f(x)=（2^x+1）/（1-3*2^x）的值域

Answer 1

设y=f(x)=（2^x+1）/（1-3*2^x）

y(1-3*2^x)=2^x+1

y-3y*2^x=2^x+1

2^x+3y*2^x=y-1

2^x*(1+3y)=y-1

2^x=(y-1)/(1+3y)

由于2^x>0,故(y-1)/(3y+1)>0

即y>1或y