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

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The discussion centers on calculating the composition of two functions, specifically f(g(x)), where f(x) = 4x + 7 and g(x) = 3x^2. The correct computation yields f(g(x)) = 12x^2 + 7, which differs from the book's answer of 12x^2 + 21x. Participants emphasize the need for clarity on the functions involved to provide accurate assistance. The discrepancy between the calculated result and the book's answer remains unresolved.
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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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