I asked this question. How can I make this better? Someone in comments is saying I should add more context but I did.
Actually, apart from the fact that you don't make the question clear in the title, it's well phrased and I disagree with the commentor. According to the question's edit history the context has been there from the start, and the major issue was with the MathJax.
But: "range of $y=f(x)$" is not a question. I think you mean "What is the range of $y=f(x)$?", but even then, your actual question is: "How do I obtain sharper bounds on $y=f(x)$?. The body of your question then states that you've used the AM-GM inequality to obtain a bound, and that you've been criticised, but not constructively, on the sharpness of your bound. So asking for help with that is a good question.
If you wanted, you could show the attempt you've made with Jensen's inequality and how that failed as that might provide insight for an answerer to explain things in ways that make more sense to you, but it's not essential.