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.