I am working on a problem where I must prove that

n log n + n + log n 2 is in theta (n log n)

part of proving this is proving that

nlogn+n+logn <=M(nlogn)

I am just completely confused on how to prove this. An example from the notes which is much simpler looks like this

example:

f (n) = 2n2 + 4 and

g(n) = n2

Show f (n) ∈ Θ(g(n))

proof:

1. let M1 = 2

2. let M2 = 4

3. let n0 = 2

4. choose any n > n0

5. ⇒ n > 2

6. ⇒ n2 > 4

7. ⇒ n2 > 2

8. ⇒ 2 < n2

9. ⇒ 4 < 2n2

10. ⇒ 2n2 + 4 < 4n2

11. ⇒ 2n2 ≤ 2n2 + 4 ≤ 4n2

12. ⇒ M1n2 ≤ 2n2 + 4 ≤ M2n2

13. ⇒ M1g(n) ≤ f (n) ≤ M2g(n)

∴ f (n) ∈ Θ(g(n))

I am just so confused because nowhere can I find any rules or steps to finding M1 and K.