1) Let g(n) = 7n + 90 and f(n) = 2n.

A) Suppose K = 3. Is there a value of N > 0 such that g(n) K f (n) for all n N ? If so, what value works? If no such value exists, explain why. B) suppose K = 5. Is there a value of N > 0 such that g(n) K f (n) for all n N ? If so, what value works? If no such value exists, explain why. C) Is g O(f)? Justify your answer using the definition.

2) Let g(n) = 3n² + 100. Use the definition to show that g O(n²). Specifically, find values of K and N that satisfy the definition, where f(n) = n².

3) Let g(n) = n³. Prove, by contradiction, that g O(n²), by completing the following steps. A) suppose, to the contrary, that g O(n²). Then the definition of big-O says that there are numbers K and N and an inequality involving K and n that must hold for all n N . Write this inequality. B) explain why the above inequality leads to a contradiction.