- #1
What are Direct and Inverse Images in Mathematics?
- Thread starter phillyolly
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Homework Help Overview
The discussion revolves around the concepts of direct and inverse images in mathematics, specifically in the context of a problem involving function composition and their properties. The original poster seeks assistance with understanding the inverse image after attempting the direct image.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss the relationship between direct and inverse images, with one suggesting a method involving function composition. There are attempts to clarify the boundaries of the inverse image and how they relate to the original function.
Discussion Status
Some participants have provided guidance on the relationship between the functions and their inverses, while others express a sense of validation in their understanding. The discussion appears to be productive, with various interpretations being explored without a clear consensus.
Contextual Notes
The original poster has shared their attempts and is working within the constraints of a homework assignment, indicating that there may be specific requirements or limitations to consider in their approach.
- #2
Raskolnikov
- 193
- 2
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
- 2
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
- 157
- 0
It turns out, I am not too dumb, yay! (Thank you for your patience, Raskolnikov.)
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