Additivity properties of asymptotic bounds

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In several slides, I found the asymptotic property called additivity as follows:




If $f = Theta(h)$ and $g = O(h)$ then $f+g = Theta(h)$.




Below a snapshot from one of this resources is shown:
enter image description here



I understand that if $ f = Theta(h)$ and $g = Theta(h)$ then $f+g = Theta(h)$.



But I can not figure out the proof for the property in the slide. Also I couldn't find a textbook that explains it. I wonder if it is a typo. If not would you please help to explain it?



Thank you.




algorithms asymptotics computer-science computational-complexity




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    up vote
    1
    down vote

    favorite
    1












    In several slides, I found the asymptotic property called additivity as follows:




    If $f = Theta(h)$ and $g = O(h)$ then $f+g = Theta(h)$.




    Below a snapshot from one of this resources is shown:
    enter image description here



    I understand that if $ f = Theta(h)$ and $g = Theta(h)$ then $f+g = Theta(h)$.



    But I can not figure out the proof for the property in the slide. Also I couldn't find a textbook that explains it. I wonder if it is a typo. If not would you please help to explain it?



    Thank you.




    algorithms asymptotics computer-science computational-complexity




    share|cite|improve this question
























      up vote
      1
      down vote

      favorite
      1









      up vote
      1
      down vote

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      1






      1





      In several slides, I found the asymptotic property called additivity as follows:




      If $f = Theta(h)$ and $g = O(h)$ then $f+g = Theta(h)$.




      Below a snapshot from one of this resources is shown:
      enter image description here



      I understand that if $ f = Theta(h)$ and $g = Theta(h)$ then $f+g = Theta(h)$.



      But I can not figure out the proof for the property in the slide. Also I couldn't find a textbook that explains it. I wonder if it is a typo. If not would you please help to explain it?



      Thank you.




      algorithms asymptotics computer-science computational-complexity




      share|cite|improve this question














      In several slides, I found the asymptotic property called additivity as follows:




      If $f = Theta(h)$ and $g = O(h)$ then $f+g = Theta(h)$.




      Below a snapshot from one of this resources is shown:
      enter image description here



      I understand that if $ f = Theta(h)$ and $g = Theta(h)$ then $f+g = Theta(h)$.



      But I can not figure out the proof for the property in the slide. Also I couldn't find a textbook that explains it. I wonder if it is a typo. If not would you please help to explain it?



      Thank you.





      algorithms asymptotics computer-science computational-complexity





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      share|cite|improve this question




      share|cite|improve this question








      edited Aug 24 at 3:52









      Jendrik Stelzner

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      asked Aug 24 at 1:15









      Crimson

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