Determine whether each of these functions is O(x2).

a) f(x)=17x +11

b) f(x) = x2 + 1000

c) f(x) = x log x

d) f(x) = x4/2

e) f(x) = 2x

f) f(x) = ⌊x⌋•⌊x⌋

Step 1: In this problem,we have to determine whether each of these functions is O(x2).

Step 2:

The definition for Big- O:

Let f and g be functions from the real numbers to the real numbers. Then f is O(g) if there are constants c and k

Such that

Let f and g be function from the integers or set of real numbers.For this condition we can say f(x) is O(g(x) if f(x) is O(g(x)) and f(x) is (g(x)).

If f(x) is O(g(x)) if and only if there are positive constant C1 ,C2, and k

C1|g(x)| C2|g(x)| where x>k