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

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SUMMARY

The discussion centers on the mathematical concept of the sum of two functions, specifically addressing the definition of (f+g)(x). It is established that the sum of two functions is valid when both functions, f and g, share the same domain. However, it is clarified that they do not necessarily need to have the same range, as demonstrated by the example sin(x) + x. This highlights the flexibility in function addition within defined domains.

PREREQUISITES
  • Understanding of basic function definitions in mathematics
  • Knowledge of domain and range concepts
  • Familiarity with function notation and operations
  • Basic trigonometric functions, specifically sine
NEXT STEPS
  • Explore the properties of function addition in detail
  • Study the implications of domain and range in function operations
  • Learn about piecewise functions and their sums
  • Investigate the behavior of trigonometric functions in combination with algebraic functions
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Mathematics students, educators, and anyone interested in understanding the properties of functions and their operations.

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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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