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 numerical answer, without explanation by John Reid)

I think your answer is correct.  h(x) is not a red herring but is used to specify that for x>0, |f(x)|+g(x) continues to be a polynomial.

Posted by Richard on 2005-05-11 00:46:07