4. Determine whether x3 is O(g(x)) for each of these functions g(x).a) g(x) = x2 b) g(x) = x3 c) g(x) = x2 + x3d) g(x) = x2 + x4 e) g(x) = 3x f ) g(x) = x3/2

2. Determine whether each of these functions is O(x2).a) f (x) = 17x + 11 b) f (x) = x2 + 1000 c) f (x) = x log xd) 42xf x  e) 2xf x  f) ) f (x) = (x3 + 2x)/(2x + 1)

1. Determine whether each of these functions is O(x).a) f (x) = 10 b) f (x) = 3x + 7 c) f (x) = x2 + x + 1 d) f (x) = 5 log x

Use the definition of “f(x) is O(g(x))” to show that 2x + 17 is O(3x).

6. Give as good a big-O estimate as possible for each of these functions.a) (n2 + 8)(n + 1) b) (n log n + n2)(n3 + 2) c) (n! + 2n)(n3 + log(n2 + 1))

Given the functions f, of, x, equals, 3, x, squaredf(x)=3x 2 and g, of, x, equals, 2, dot, 4, to the power xg(x)=2⋅4 x , which of the following statements is true?AnswerAttempt 1 out of 2The number of attempts on this specific problem before you are marked incorrectMultiple Choice Answersf, of, 3, equals, g, of, 3f(3)=g(3)f, of, 3, is greater than, g, of, 3f(3)>g(3)f, of, 3, is less than, g, of, 3f(3)<g(3)