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

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The discussion centers on the composition of functions, specifically calculating (f•g)(x) as f(g(x)). Given the functions f(x) = 4x + 7 and g(x) = 3x^2, the correct simplification yields f(g(x)) = 12x^2 + 7. However, this result does not match the book's answer of 12x^2 + 21x. The discrepancy highlights the importance of clearly defining the functions involved in function composition.

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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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