函数y=(x²-1)/(x²+1)的值域是···

Question

函数y=(x²-1)/(x²+1)的值域是···

Answer 1

y=(x2-1)/(x2+1)
两边同乘以 x2+1 得：
y(x2+1)=x2-1
去括号 y*x2+y=x2-1
移项 y*x2-x2+y+1=0
(y-1)x2+y+1=0
x为实数,x的方程有实数解,Δ≥0
Δ= 0-4*(y-1)(y+1)≥0
4*(y-1)(y+1)≤0
(y-1)(y+1)≤0
-1≤ y ≤ 1
所以y的取值范围是-1≤ y ≤ 1,即值域为 -1≤ y ≤ 1.