Please answer the a, b and c parts. Last time someone only answered the d part.

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Please answer the a, b and c parts. Last time someone only answered the d part. I am posting this question again, so only provide me with an answer if you know all the three parts.

Problem 1 (20 pts, 5 each) Let f(n) and g(n) be two functions from Nt to Rt. Prove or disprove the following assertions. To disprove, you only need to give a counter example for functions n) and/or g(n) which make the assertion false. (a) 2(e (f (m))) (f (n)). (b) w (o (m))) o(w(f(n))). (c) If f(n) 3e(g(m)), then 2f (29 n)). (d) f(n) +g(n) max(f (n), gin

Explanation / Answer

a) let f(x) = 6x4 2x3 + 5 and g(x) = x4. Applying the formal definition from above, the statement that f(x) = O(x4) is equivalent to its expansion,

for some suitable choice of x0 and M and for all x > x0. To prove this, let x0 = 1 and M = 13. Then, for all x > x0:

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