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've only started looking at this problem, but it seems to me that h(x) actually does serve a purpose.

If h(x) is a polynomial, and g(x) is a polynomial, then |f(x)| must also be a polynomial.  Either f(x) is all positive or all negative in the given range (it may include 0).  Or perhaps there is some other possibility that I haven't thought of.

Edit:  Nevermind.  I take back what I said.

Edited on May 10, 2005, 9:46 pm

Edited on May 10, 2005, 10:00 pm

Posted by Tristan on 2005-05-10 21:46:04