Question

7. Let f(x) = 3x + 4. We know that f(x) is big-O of x2. Find the lowest k that works for C = 1 and justify your answer fully. Note that you have to show two aspects: your k works and the no lower k value work.

Important: you must show all work on free response questions. If the question asks you to prove something, you must write a proof as explained in the presentations and additional handouts on proofs.

Answer 1

Thus, for f(x) <= c g(x) to hold, x must be greater then 4 or less then -1, but not between -1 and 4.

Since, we need a k such that all x greater then it must satisfy the above relation, x must be >= 4.

Thus, k = 4 is the required answer.  

Given f(x) = 3x+4 c=1 here, glu) = x we know that If (alle clg call for all a zk. so laxaul < c/ +21 е knоw с г |3xtul { l/m2) 13x+41 <1x²9 (tx² 3x-412o. so x²-3x-420 x-4x+x-420 x (x-4)+1(arul 20 (x-4) (4+11 20 N-420 x+120 x24 ,nar : minimom value of kis 4.