https://file.aiquickdraw.com/mathbot/file/172668394191614hi9k9j.jpg

In the image you uploaded, you have the functions \( f(x) = 3x + 4 \) and \( g(x) = 5x^2 + 2x \). You are tasked with finding the composition of the functions, denoted as \( (f \circ g)(x) \), which means \( f(g(x)) \).

Let's calculate \( f(g(x)) \):

1. Substitute \( g(x) \) into \( f(x) \):
   \[
   f(g(x)) = f(5x^2 + 2x)
   \]
   
2. Replace \( x \) in \( f(x) \) with \( 5x^2 + 2x \):
   \[
   f(5x^2 + 2x) = 3(5x^2 + 2x) + 4
   \]
   
3. Distribute and simplify:
   \[
   3(5x^2 + 2x) + 4 = 15x^2 + 6x + 4
   \]

So, the composition \( (f \circ g)(x) \) is \( 15x^2 + 6x + 4 \).

If you have any further questions or need more details on this process, feel free to ask!

#### Related Questions:
1. What is the graphical interpretation of the composition of functions?
2. Can you determine \( (g \circ f)(x) \) using the same functions?
3. What happens if the order of composition is reversed?
4. How do compositions affect the domain and range of the resulting function?
5. Is there a real-life scenario where composition of functions is applied?

#### Tip:
When solving for a function composition, always substitute the entire function for each instance of \( x \) in the outer function and then simplify.

Given the functions f(x) = 3x + 4 and g(x) = 5x^2 + 2x, what is the simplified expression for the composition (f o g)(x)?

Explore how to compute the composition of the functions f(x) = 3x + 4 and g(x) = 5x^2 + 2x, resulting in a simplified polynomial expression. This tutorial is ideal for college students studying advanced algebra or precalculus.

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