Intersecting Bivariate Functions: Is x=a the Only Point of Intersection?

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  • Thread starter Saracen Rue
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In summary, the bivariate function f(x,a) and f(a,x) will always intersect at the point x=a, as this is the case when the two functions are equal. This holds true even if there are other points of intersection, as they are not relevant to the question. The given scenario of a=x, b=a', c=a', d=x and a'=x results in f(x,x) = f(x,x), which is a trivial case.
  • #1
Saracen Rue
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Will the bivariate function ##f(x,a)## always intersect ##f(a,x)## at the point ##x=a## given that ##f## is a real, defined function? (other points of intersection can exist but are not relevant for this question)
 
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  • #2
Hey Saracen Rue.

If you have an intersection then it means that the two things are equal.

So if you had a bivariate function with points (a,b) and (c,d) then an intersection happens when f(a,b) = f(c,d)

You have specified [if I read correctly] that a=x, b=a', c=a', d=x and a'=x meaning that you have f(x,x) = f(x,x) which is trivial.

Are we missing something here?
 
  • #3
Didn't we answer that question in your earlier thread already?
 

1. What is a simple intersection question?

A simple intersection question is a type of question that asks about the relationship between two or more ideas, concepts, or variables. It typically involves finding common ground or overlap between the different elements being compared.

2. How do you identify a simple intersection question?

A simple intersection question can often be identified by the use of words such as "and," "both," "similar," or "in common." It may also involve comparing two or more different categories or ideas.

3. What is the purpose of a simple intersection question?

The purpose of a simple intersection question is to explore the connections and relationships between different elements. It can help to clarify similarities and differences, and can also be used to generate new ideas or perspectives.

4. How do you answer a simple intersection question?

To answer a simple intersection question, you will need to identify the common elements between the different ideas or variables being compared. This can often be done by creating a Venn diagram or making a list of shared characteristics.

5. How can simple intersection questions be used in scientific research?

Simple intersection questions can be used in a variety of ways in scientific research. They can help to identify patterns or relationships between different variables, and can also be used to develop new hypotheses or theories. Additionally, they can be used to compare and contrast different studies or findings in a particular field of research.

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