Show that fx O x2 by defintion of BigOh find such constants

Show that f(x) = O (x^2) \"by defintion\" of Big-Oh (find such constants that necessary inequality holds):

Solution

f(x) = x^2 + 5x - 3

To show f(x) is O(g(x)) we must show constants C and k such that f(x) <= C * g(x) for all x >=k

x^2 + 5x - 3 <= Cx^2
Putting C = 2,

We see that the above expression is true for all x >= 2

So,
x^2 + 5x - 3 is Big-oh