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

In summary, the question wants (f•g)(x) to be simplified. To do this, we need to plug the value of g(x) into every x in f(x) and then simplify. The functions provided are f(x) = 4x + 7 and g(x) = 3x^2. After plugging in g(x) into f(x), we get f(g(x)) = 12x^2 + 7. This is different from the book's answer of 12x^2 + 21x.
  • #1
mathdad
1,283
1
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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  • #2
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
 
  • #3
f(x) = 4x + 7

g(x) = 3x^2
 
  • #4
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" ?
 
  • #5
Book's answer:

12x^2+21x.
 

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

What is the definition of composition of functions?

The composition of functions is a mathematical operation that combines two functions to form a new function. It is denoted by (f ∘ g)(x) and read as "f composed with g of x". The output of one function becomes the input of the other function, resulting in a new output.

What is the domain and range of a composite function?

The domain of a composite function is the set of all the inputs for which the composite function is defined. The range of a composite function is the set of all the outputs that are obtained when all possible inputs are used.

What is the difference between a composite function and a simple function?

A simple function is a function that has only one input and one output. A composite function is formed by combining two or more simple functions. In a composite function, the output of one function becomes the input of the other function, while in a simple function, the input and output are independent.

What is the purpose of using composition of functions?

The purpose of using composition of functions is to simplify complex mathematical expressions and to model real-world situations. It also allows us to break down a complex problem into smaller, more manageable parts.

Can any two functions be composed together?

No, not all functions can be composed together. For a composite function to be defined, the output of one function must be in the domain of the other function. If this condition is not met, the composition is not defined and the two functions cannot be composed together.

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