Inputs and outputs of composite function

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Homework Help Overview

The discussion revolves around understanding the domain and range of composite functions, specifically in the context of functions such as f(g(x)). Participants are exploring how to determine these properties and the implications of function composition.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants attempt to clarify the process of finding the domain and range of composite functions, questioning how the range of one function relates to the domain of another. There are discussions about specific examples and the implications of function behavior, such as increasing functions and their ranges.

Discussion Status

The discussion is active with multiple participants contributing different perspectives and examples. Some participants are seeking clarification on specific points, while others are providing insights into the behavior of functions and their ranges. There is no explicit consensus, but various interpretations and approaches are being explored.

Contextual Notes

Participants are working within the constraints of homework guidelines, which may limit the depth of exploration. Some questions remain about specific function behaviors and the implications of their ranges, indicating areas where further clarification is needed.

  • #31
Coco12 said:
U plug in x into the equation to find out what numbers y is greater than or equal to and same for the 3
"Textspeak" isn't allowed here. Please don't write "u" for "you".
 
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  • #32
scurty said:
Okay, that makes sense now. You plug the x values into the equation, not the range.
So you plug in x values into equation to get the range? Does this always work. Because I know in some cases the domain is all real numbers but the range might not be.
 
  • #33
Coco12 said:
So you plug in x values into equation to get the range? Does this always work. Because I know in some cases the domain is all real numbers but the range might not be.

Why would that invalidate it? If the number you plug in is part of the domain then the number you get out must be part of the range.
 

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