Are the Sum of Two Functions Always Equal to the Sum of their Individual Parts?

  • Context: Undergrad 
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Discussion Overview

The discussion centers around the mathematical concept of the sum of two functions, specifically whether the sum of two functions is always equal to the sum of their individual parts. The scope includes definitions and conditions under which this concept holds true.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks for clarification on the definition of (f+g)(x) and how it is being defined.
  • Another participant states that the definition of the sum of two functions is valid as long as f and g have the same domains and ranges.
  • A later reply challenges the previous assertion by stating that the functions do not need to have the same range, providing the example of sin(x) + x.

Areas of Agreement / Disagreement

Participants express differing views on the requirements for the sum of two functions, particularly regarding the necessity of having the same range, indicating that multiple competing views remain in the discussion.

Contextual Notes

There are unresolved aspects regarding the definitions and conditions under which the sum of two functions is considered valid, particularly concerning domains and ranges.

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where f and g are finctions of x

please thanks
 
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you mean "functions"...
 
that's a definition as far as I am concerned. How are you defining (f+g)(x)?
 
This appears to be the definition of the sum of two functions. It is valid as long as f and g have the same domains and ranges.
 
ObsessiveMathsFreak said:
This appears to be the definition of the sum of two functions. It is valid as long as f and g have the same domains and ranges.

They don't need the same range.

Try sin(x) + x.
 

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