- #1

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- TL;DR Summary
- Why in combining functions to form other functions do we restrict the domain to the intersections of their domains?

For example:

h(x)=f(x)+g(x)

If f(x) and g(x) are real numbers and real numbers can be added, subtracted, multiplied and divided (except by 0). why do we insist that the x in f(x) and g(x) be {x: x∈ dom f ∩ dom g}?

My thoughts:

The equality of two functions requires two criteria:

1) They operate on the same domain

2) Images be the same, element for element

Criteria 1) is not satisfied if x does not belong to the intersection of the two sets

then f(x1)+g(x2)=h(x3, x2 or x1)

h is mapping a different element in the domain to that of f or g yielding the same image resulting from any operation we perform on f and g.

h(x)=f(x)+g(x)

If f(x) and g(x) are real numbers and real numbers can be added, subtracted, multiplied and divided (except by 0). why do we insist that the x in f(x) and g(x) be {x: x∈ dom f ∩ dom g}?

My thoughts:

The equality of two functions requires two criteria:

1) They operate on the same domain

2) Images be the same, element for element

Criteria 1) is not satisfied if x does not belong to the intersection of the two sets

then f(x1)+g(x2)=h(x3, x2 or x1)

h is mapping a different element in the domain to that of f or g yielding the same image resulting from any operation we perform on f and g.