Help with Understanding Composite Functions

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    Composite Functions
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Homework Help Overview

The discussion revolves around understanding composite functions, specifically the composition of two functions, f and g. The original poster expresses confusion regarding the concept of composite functions and how to determine their domain.

Discussion Character

  • Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants explore the definition of composite functions, with some attempting to clarify that composition involves substituting the output of one function into another. Questions arise about whether the composite function is simply one of the functions or a product of both.

Discussion Status

The discussion is active, with participants providing clarifications about the nature of composite functions. There is an emphasis on understanding the correct notation and process for composition, though no consensus has been reached on the original poster's specific confusion.

Contextual Notes

The original poster mentions a lack of equations and expresses uncertainty about the domain of the composite function, indicating potential gaps in foundational understanding.

frozenbananas
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Homework Statement



posted in title

Homework Equations



none

The Attempt at a Solution


f+g would be

(2x^2+1) + (x-1) = 2x^2 + x so the domain for f+g is all real numbers but i don't know how to find the one for the composite. i am still confused as to what a composite function is, please help me! thank you!
 
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composition of f&g is nothing but f o g which is the same as fg or f(g(x)).

So take the entire g(x) and put it wherever you see 'x' in f.
 


the composite is simply g then? or is it f(x) multiplied by g(x)?
 


frozenbananas said:
the composite is simply g then? or is it f(x) multiplied by g(x)?

As rock.freak said, it is f(g(x)), not g(x). 'x' is the input to g and then the output g(x) becomes the input to f. It is different to multiplying.

As an example: If g(x)=x+x^2 and f(x)=2x, then the composition gf(x) = 2x + (2x)^2
 

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