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To find \((f \circ g)(x)\), or \(f(g(x))\), you need to substitute \(g(x)\) into the function \(f(x)\).

Given:
- \(f(x) = 5x + 4\)
- \(g(x) = 4x^2 + 2x\)

Substitute \(g(x)\) into \(f(x)\):
\[
f(g(x)) = 5(4x^2 + 2x) + 4
\]

Now, expand and simplify:
\[
f(g(x)) = 5 \cdot 4x^2 + 5 \cdot 2x + 4 = 20x^2 + 10x + 4
\]

So, the simplified expression is:
\[
(f \circ g)(x) = 20x^2 + 10x + 4
\]

Would you like more details or have any questions?

Here are some related questions to explore:

1. How would you find \((g \circ f)(x)\) using the same functions?
2. What is the domain of the function \((f \circ g)(x)\)?
3. How do the degrees of the functions \(f(x)\) and \(g(x)\) affect the degree of \((f \circ g)(x)\)?
4. Can you find the derivative of \((f \circ g)(x)\)?
5. What would \((f \circ g)(2)\) be if \(x = 2\)?

**Tip:** When composing functions, always substitute the inner function into the outer one before simplifying.

Let f(x) = 5x + 4 and g(x) = 4x^2 + 2x. After simplifying, (f(g(x)) = ?

Learn how to simplify the composition of functions f(x) = 5x + 4 and g(x) = 4x^2 + 2x. This problem involves key algebraic concepts such as function composition and polynomial expansion, suitable for students in Grades 9-12.

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