Recall that in big-O notation we say f(x) is O (x^4) if here exist real numbers C and k (called witnesses) such that |f(x)| lessthanorequalto C middot x^d for all x > k. Using the symbols of formal logic, exist C exist k Forall x (x > k rightarrow |f(x)| lessthanorequalto C middot x^d). Note that C and k cannot depend on x, but they can depend on d. (a) Prove that f(x) = x^2 + x + 1 is O (x^2) using the definition of O(x^d) (b) Prove that g(x) = x^d+1 - 1/x - 1 is O(x^d)