Question

求大神解道高一数学题~~~~T T

Y=(1+X^2)/(1-X^2)的值域

过程详细点，谢谢咯~~

Answer 1

y=(x^2-1+2)/(1-x^2)=-1+2/(1-x^2)
因为1-x^2<=1,所以2/(1-x^2)>=2或 2/(1-x^2)<0
故y>=-1+2=1或y<-1
值域为y>=1或y<-1

Answer 2

Y=(1+X^2)/(1-X^2)
(1-X^2)Y=（1+X^2)
整理得 （1+Y）X^2+1-Y=0
看成关于X的2次方程
则 贝塔=0-4（1+Y）（1-Y）大于等于0
1-Y^2小于等于0
解得 Y小于等于-1或大于等于1

Answer 3

将函数变形得y=-1+2/(1-x^2),因为x^2>=0,1-x^2<=1,1/(1-x^2)<=0 或1/(1-x^2)>=1，所以2/(1-x^2)<=0 或2/(1-x^2)>=2,所以y<=-1或y>=1