试用两种方法求函数f(x)=x^2/（x^2+1）的值域

Question

试用两种方法求函数f(x)=x^2/（x^2+1）的值域

Answer 1

1、设y=X^2/(X^2+1),(y≥0,y≠1)
则(1-y)X^2=y,X^2=y/(1-y)
Y/(1-Y)≥0得0≤y≤1,∴0≤y