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I have been trying to solve the following problem for more than a week without any success.

Given the function: $$f(x)=\frac{x^2+mx+4}{x^2+x+4}$$ Find all possible values of the parameter $m$ such that for any three numbers $a,b,c$ the corresponding values of the function $f(a),f(b)$ and $f(c)$ are sides of a triangle.

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    The use of subjective assessments like "easy", "hard", "tricky" is in my view not helpful in summarizing the problem to others in the title because perceptions about the difficulty of problems vary widely. Please consider replacing the title with a more specific and less subjective summary of the question, such as "Parameter values that make function values side lengths of a triangle".2012-11-13
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    Personally, I like it when mathematicians give their opinions about what's easy and what's hard, and I wish it were more common. Even if I disagree with them, it helps put things in perspective.2012-11-13
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    I am an artist not a mathematician. Sorry about that.2012-11-13
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    @littleO: I wasn't arguing against giving opinions about that, only against placing them in the title. I agree that information about what appears easy or hard to the person asking the question can be helpful in answering it. However, that information is unlikely to be informative to someone scanning the question titles on the main page for questions of interest.2012-11-13

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