Prove Max(f(n),g(n))= Theta(f(n)+g(n))

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problem on asymptotic notations,

Prove Max(f(n),g(n))= Theta(f(n)+g(n)) using the theorom proved in last video.
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Thank you! You just saved me from hours of confusion :)

moonstruck
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EDIT: Repost but here are the steps in another way as the video:

We know that 𝑓(𝑛)=Θ(𝑔(𝑛)) means 𝑓(𝑛)=𝑂(𝑔(𝑛)) and similarly 𝑓(𝑛)=Ω(𝑔(𝑛))

So now just need to choose c values to try for first time:
𝑚{𝑓, 𝑔}=𝑂(𝑓+𝑔) letting 𝑐>0
𝑓+𝑔=𝑂(𝑚{𝑓, 𝑔}) letting 𝑐≥2

So,

𝑓=𝑂(𝑔) where 𝑐>0
Similarly: 𝑔=𝑂(𝑓) where 𝑐≥2 which ⟹𝑓=Ω(𝑔)
Which ⟹𝑓=Θ(𝑔)

lydiadeshmukh
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Thanks. It was easy to understand at 2x Speed 👍

TheSumitBanik
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Thanks for this video mam, this helped a lot

rishabhpandeyaroll.
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How u wrote... t(n) and h(n)... in the denominator... in the last step?

therealhustlerSG