Tell whether each of the following statements is true or false.  explanation is needed. if f (n) = O(g(n)) then f (n) = Θ(g(n)) if f (n) = O(g(n)) then g(n) = Ω(f (n)) if f (n) = Θ(g(n)) then g(n) = Ω(f (n))

How would you use part a to find out part b?

(8) Find the value of c guaranteed by the Mean Value Theorem for f(x) [3, 5]. (A) 1+ 2√2 (B) 2√2 (C)1-2√2 For Questions 9-10, consider a particle whose motion is represented by the position function s(t) = t²-t, t≥ 0, where s is in feet and t is in seconds. (9) The particle moves forward when (A) t > 2 (B)t>1 (D) 3 (A) s(2) — s(0) = 2 ft. (C) s(2) s() = 2/1/1 2²/1 (10) The distance traveled by the particle in the first two seconds 1 (C)t> (C)t> ½ (D) It always moves backward. 2 on the interval (B) |s(2) — s( ½|+|s() - s(0)| = 2/2 + 1/2 = 2/1/2 (D) cannot be determined

Question 7. Let f: R → R and g: R → R be of the form f(x) = = ax + b and g(x) = cx + d where a, b, c and d are constants. Determine necessary and sufficient conditions on the constants a, b, c and d so that fog=gof Justify your answer.