Question

Big-O Notation - Show that f(x) = x^2 + 2x + 1 is O(x^2)

Answer 1

I am not able to understand this in my textbook. The solution says we observe that we can readily estimate the size of f(x) when x > 1 because x < x^2 and 1 < x^2 when x > 1. It follows that 0 <= x^2 +2x + 1 <= x^2 +2x^2 + x^2 = 4x^2

By that example, I see that the constant C is 4 and k is 1. However, I don't understand at all why they just decided to throw x2 everywhere and then sum the coefficients to get 4 as the answer for C.