What is the result of adding f and g in set addition?

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Discussion Overview

The discussion revolves around the operation of adding two sets, f and g, in the context of set addition versus function addition. Participants explore the implications of both interpretations and how they affect the resulting outputs.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Post 1 presents the sets f and g and asks for the result of their addition.
  • Post 3 expresses confusion regarding the nature of the addition, suggesting a misunderstanding of the operation.
  • Post 4 prompts for the evaluation of the functions f and g at a specific input, -4, to clarify the addition process.
  • Post 5 proposes a potential output of (-8,6), indicating a misunderstanding of the addition process.
  • Post 6 clarifies that the input remains -4, and the outputs of f and g at that input should be summed, resulting in (-4, 6).
  • Post 7 questions whether the operation is a union of sets or the addition of functions, highlighting ambiguity in the question.
  • Post 9 discusses the implications of adding outputs from two functions, noting that undefined outputs can complicate the addition process.
  • Post 11 reiterates the necessity of using the same input value for both functions to compute their sum correctly.

Areas of Agreement / Disagreement

Participants express differing interpretations of the operation, with some believing it refers to function addition and others considering set union. The discussion remains unresolved regarding the intended meaning of "adding" the sets f and g.

Contextual Notes

The discussion highlights ambiguities in the question regarding whether it refers to set union or function addition, and the implications of undefined outputs when the functions are not defined for the same inputs.

thomasrules
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Let f = {(-4.4),(-2,4),(1,3),(3,5),(4,6)}

and g = {(-4,2),(-2,1),(0,2),(1,2),(2,2),(4,4)}

Determine a)f + g
 
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What are your thoughts?

- Warren
 
honestly I'm confused...
f(x)=-4x+4? etc...?
It's not (-4,4)+(-4,2)
 
What's the value of the function f at, say, -4?

What's the value of the function g with the same input, -4?

What's the sum of the values of the two functions, given the same input, -4?

- Warren
 
wouldn't it be (-8,6)
 
No, the input -- the value on the left -- is still -4. The summed outputs of both functions, however, is indeed 4+2 = 6.

You have thus found the first input-output pair of the sum of f+g, (-4, 6).

In english, this means if you plug -4 into f(x) + g(x), you get f(-4) + g(-4) = 4+2 = 6.

- Warren
 
Is this adding two sets f and g or is this adding function f to function g? The way it's written I assumed it was creating a union of two sets.
 
but what's the equation of f(x)=?
It looks like you set x to zero

why does left side -4 stay the same ...?
 
Last edited:
daveb,

You have a good point. This question is a little ambiguous. However, simply taking the union of two sets means that the resulting function f+g is multivalued at -4, for example, which means it's no longer a function.

Adding the outputs of the two functions is also a little tricky, since f is defined at 3, for example, while g is not. The sum of the two functions at 3 is thus also undefined, since anything + undefined = undefined.

The first set is f(x), for x values -4, -2, 1, 3, and 4.

The second set is g(x), for x values -4, -2, 0, 1, 2, and 4.

The only input values common to both functions are -4, -2, 1, and 4. These are thus the input values acceptable to the function f+g. All other possible input values have no defined output.

The output values of f+g are each the sum of the outputs of f and g at the same point. Thus, if you plug in -4 to f+g, you get f(-4) + g(-4) = 4+2 = 6.

- Warren
 
  • #10
oh so ur saying that when adding them you have to have the same x value
 
  • #11
Yes. When you give the function f the input -4, it produces the output 4. When you give the function g the input -4, it produces the output 2.

When you give the sum of the two functions, f+g, the input -4, the result is the sum of the outputs, 4+2 = 6.

Thus, one member of the resulting set for f+g should be (-4, 6).

- Warren
 
  • #12
thank you my friend
 

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