For all x in the given ranges, polynomials f, g, and h satisfy the following equations:

|f(x)| + g(x) = 4x, x ≤ -2;
|f(x)| + g(x) = -2x², -2 < x ≤ 0;
|f(x)| + g(x) = h(x), x > 0;

What is the least possible value of f(10)?

(In reply to re: numerical answer, without explanation by Richard)

The problem states directly that f, g and h are polinomials. It says "..., polinomials f, g, and h satisfy...". In particular, it does not state that they are polinomials in this or that particular region.

I still don't understand the need for the last equation, since as people have said, the first two equations determine f(x) up to an overall sign.

Posted by ajosin on 2005-05-11 16:06:29