How Do We Calculate (f O g) for Given Functions and Set A?

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Discussion Overview

The discussion centers on calculating the composition of two functions, f and g, defined on a set A. Participants explore how to derive the function h, which represents the composition of f and g.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant provides the definitions of the functions f and g and asks how to calculate the composition (f O g).
  • Another participant explains the process of finding h(x) by first applying g to x and then applying f to the result.
  • A participant attempts to calculate h(1) and presents their reasoning, suggesting that h(1) = 3 based on their calculations.
  • One participant confirms the correctness of the previous calculation.
  • A later reply reiterates that h can be viewed as shorthand for the function defined by h(x) = f(g(x)).

Areas of Agreement / Disagreement

Participants generally agree on the method for calculating the composition of the functions, but there is no explicit consensus on the overall understanding of the composition process beyond the individual calculations presented.

Contextual Notes

Some assumptions about the definitions of the functions and their domains may not be fully articulated, and the discussion does not address potential edge cases or broader implications of function composition.

aaa59
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if A={1,2,3}

f:A-> A = {(1,2),(2,3),(3,1)}
g:A->A = {(1,2),(2,1),(3,3)}

how would we calculate (f O g)?
 
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say h = f o g. To find h(x), simply plug x into g, and then plug the result into f.

For example, g(2) = 1 and f(1) = 2. So h(2) = 2. Hope this helps.
 
i think i got it.

so: g(1) = 2 and f(2) = 3. therefore h(1)=3. am i right?
 
Yes.
 
At this stage, you can just consider
[tex]h = f \circ g[/tex]
as just "shorthand" for the function defined by
[tex]h(x) = f(g(x))[/tex]
 

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