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)?
From some quick calculations, I'm coming up with -120 as the minimum possible value of f(10).
By the way, this problem had me stumped originally, until I realised that we were told that f, g and h were polynomials, and not just any old run-of-the-mill-garden-variety functions.
Questions: a) Is my answer correct?... and b) Why did we need to have reference to the function h(x) in the problem? Seems to me it was just a red herring.
Thanks Charlie!
numerical answer, without explanation
