Asymptotic analysis of functions

Question

I have the following function to prove that its time complexity is less or equal to O(xlogx)

f(x) =xlogx+3logx2

I need some help to solve this.

I did understand your solution but how you have made x log x > = 6 log x ? — Zeeshan shaikh, Mar 08 '15 at 19:28
i have another function to prove , if you can help me out in that also ? — Zeeshan shaikh, Mar 08 '15 at 19:35

Am_I_Helpful · Accepted Answer · 2015-03-08T19:27:48.240

3

Given,

   f(x) = xlogx+3logx^2
        = xlogx+6logx   // since log (a^b) = b log a

As we know, f(x) = O(g(x)), if | f(x) | <= M. | g(x) |, where M is a positive real number.

Therefore, for M>=7 and x varying in the real positive range,

M . x log x >= x log x + 6 log x
            >= (x+6) log x.

f(x) = x log x + 3log x^2 
     = O(x log x).

edited Mar 08 '15 at 19:27

answered Mar 08 '15 at 19:21

Am_I_Helpful

1 Answers1