What is the Result of Plugging g(x) Into f(x)?

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    Composition Functions
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Discussion Overview

The discussion revolves around the composition of two functions, f(x) and g(x), specifically evaluating f(g(x)). Participants explore the process of substituting g(x) into f(x) and simplifying the result, while also comparing their findings to a provided book answer.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • Some participants assert that (f•g)(x) is interpreted as f(g(x)), leading to the substitution of g(x) into f(x).
  • One participant calculates f(g(x)) as 12x^2 + 7, based on their definitions of f(x) and g(x).
  • Another participant questions the correctness of the calculated result by asking for the "book answer."
  • The book answer is stated as 12x^2 + 21x, which does not match the calculated result.

Areas of Agreement / Disagreement

Participants generally agree on the method of composition but disagree on the correctness of the calculated result compared to the book answer. The discussion remains unresolved regarding the discrepancy between the two results.

Contextual Notes

The discussion lacks clarity on the definitions of the functions and the context of the book answer, which may depend on specific assumptions or interpretations not fully articulated by participants.

mathdad
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The question wants (f•g)(x). I understand this to be
f(g(x)).

This means to plug the value of g(x) into every x I see in f(x) and simplify.

f(3x^2) = 4(3x^2) + 7

f(3x^2) = 12x^2 + 7

So, f(g(x)) = 12x^2 + 7.

This is not the book's answer.
 
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RTCNTC said:
The question wants (f•g)(x). I understand this to be
f(g(x)).

This means to plug the value of g(x) into every x I see in f(x) and simplify.

f(3x^2) = 4(3x^2) + 7

f(3x^2) = 12x^2 + 7

So, f(g(x)) = 12x^2 + 7.

This is not the book's answer.
What are your functions f(x), g(x)? Can't help you if we don't know that! Please give us the whole problem.

-Dan
 
f(x) = 4x + 7

g(x) = 3x^2
 
f(x) = 4x + 7

g(x) = 3x^2

So, f(g(x)) = 12x^2 + 7.

This is not the book's answer.

For the two functions you cite, your solution is correct ... what is the "book answer" ?
 
Book's answer:

12x^2+21x.
 

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