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T1(n) = ϴ(f(n)) means T1(n) and f(n) are asymptotically equal.  

similarly, T2(n) = ϴ(f(n)) means T2(n) and f(n) are asymptotically equal.  

so T1(n) + T2(n) is also asymptotically equal to f(n). which is allowed in big Oh.

T1(n) + T2(n) = ϴ(f(n)) and

T1(n) + T2(n) = O(f(n)) both statements are true
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 T1(n) + T2(n) = max ( T1, T2 ) i.e when two functions are merged then final time complexity becomes the maximum of the time complexity of two functions

hence  T1(n)+T2(n) = 0(f(n))

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