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What are Direct and Inverse Images in Mathematics?
- Thread starter phillyolly
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In summary, the conversation is about seeking help with inverse image for a given problem. The person seeking help has correctly completed part (a) and is now looking for guidance on part (b). The suggested method is to look at the boundaries of G to determine the boundaries of its inverse image. The conversation ends with the person receiving help reassuring themselves that they have solved the problem correctly.
- #2
Raskolnikov
- 193
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You did part (a) correctly!
Part (b):
If [tex] h = g \circ f, [/tex] then [tex] h^{-1} = f^{-1} \circ g^{-1}. [/tex]
Look at the boundaries of G. They will give you the boundaries of its inverse image. This isn't ALWAYS the case, but our function here is pretty simple so it will work out well.
Part (b):
If [tex] h = g \circ f, [/tex] then [tex] h^{-1} = f^{-1} \circ g^{-1}. [/tex]
Look at the boundaries of G. They will give you the boundaries of its inverse image. This isn't ALWAYS the case, but our function here is pretty simple so it will work out well.
- #3
- #4
Raskolnikov
- 193
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mhmm! and a nice self-assuring way to check that you "almost definitely" got it right is the fact that [tex] f(\{x : -2 \le x \le 0\}) = G. [/tex] I say "almost definitely" because it could happen that you luck out and it works even though your answer's wrong...but let's not worry about that haha. you got it right!
- #5
phillyolly
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It turns out, I am not too dumb, yay! (Thank you for your patience, Raskolnikov.)
1. What is meant by "direct/inverse images" in science?
Direct and inverse images refer to the relationship between two sets of data. The direct image of a set A is the set of all elements that are mapped from set A by a given function. The inverse image of a set B is the set of all elements that are mapped to set B by the same function.
2. Why is finding direct/inverse images important in scientific research?
Finding direct/inverse images is important because it allows scientists to understand the relationship between different sets of data. This can help in identifying patterns, making predictions, and drawing conclusions in a variety of scientific fields.
3. How do scientists find direct/inverse images?
To find direct/inverse images, scientists use mathematical functions to map elements from one set to another. This can be done by hand or with the help of computer software. The resulting sets of data can then be analyzed to gain a deeper understanding of the relationship between the two sets.
4. What are some practical applications of direct/inverse images in science?
Direct/inverse images have many practical applications in science, including data analysis, modeling, and prediction. For example, in genetics, scientists use direct/inverse images to study the relationship between different genes and traits. In physics, they use it to understand the relationship between different physical quantities.
5. Can direct/inverse images be used in other fields besides science?
Yes, the concept of direct/inverse images can be applied in other fields, such as mathematics, engineering, and economics. Any discipline that involves the analysis of data and relationships between different variables can benefit from using direct/inverse images to gain a deeper understanding of the data.
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