To find the range of the function y = x ^ 2 / x ^ 2 + 1 (the square of x plus the square of 1 / 2 of x), I use x ^ 2 = Y / y + 1 to find the range of [0.1] Then I use another method to change the original formula to 1 / y = 1 + 1 / x ^ 2, but the result is wrong. What's wrong with this method? I know how to calculate it. I use the second method to solve 1 / 2, but I just can't figure out what's wrong with the second method.

To find the range of the function y = x ^ 2 / x ^ 2 + 1 (the square of x plus the square of 1 / 2 of x), I use x ^ 2 = Y / y + 1 to find the range of [0.1] Then I use another method to change the original formula to 1 / y = 1 + 1 / x ^ 2, but the result is wrong. What's wrong with this method? I know how to calculate it. I use the second method to solve 1 / 2, but I just can't figure out what's wrong with the second method.

y=x^2/(x^2+1)
=(x^2+1-1)/(x^2+1)
=1-1/(x^2+1)
Because x ^ 2 > = 0
x^2+1>=1
0=-1
therefore
1>y=1-1/(x^2+1)>=0
So the domain is [0,1]