[Catphish]

Actually, the range of y=f(x)=x+2/x is the set of all y whose absolute value is less than or equal to the square root of 8.

You just set 2+2/x=y, turn it into a quadratic equation in x and then compute discriminant, y^2-8.

[Catphish]

I meant “whose absolute value is greater than or equal to 8”

[Bob]

Actually, the range of y=f(x)=x+2/x is the set of all y whose absolute value is less than or equal to the square root of 8.

You just set 2+2/x=y, turn it into a quadratic equation in x and then compute discriminant, y^2-8.

Sorry, you lost me at "turn it into a quadratic equation in x". How would you do that? (As I said earlier, I'm no mathematician.)