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The problem asks to evaluate the composition of functions \( (g \circ f)(x) \) for \( x = 3 \), where:

\[
f(x) = x^3 + 8x, \quad g(x) = \sqrt{5x}, \quad h(x) = 3x + 4
\]

### Step-by-step solution:

1. **First, compute \( f(3) \):**

\[
f(3) = 3^3 + 8 \times 3 = 27 + 24 = 51
\]

2. **Next, compute \( g(f(3)) \), which is \( g(51) \):**

\[
g(51) = \sqrt{5 \times 51} = \sqrt{255}
\]

Since \( \sqrt{255} \) cannot be simplified further, the final answer is:

\[
(g \circ f)(3) = \sqrt{255}
\]

Let me know if you need more details or have questions.

Here are 5 related questions to explore:
1. How do you find the composition of functions in general?
2. How does the domain of a composition of functions affect its evaluation?
3. Can you simplify the square root of 255 any further?
4. How would the result change if \( f(x) \) was a different polynomial?
5. What is the significance of function composition in real-world problems?

**Tip:** When solving composition of functions, always calculate from the innermost function outward!

Evaluate the function (g ∘ f)(x) for x = 3 where f(x) = x^3 + 8x, g(x) = √(5x), h(x) = 3x + 4.

Learn how to evaluate the composition of functions (g ∘ f)(x) for x = 3 where f(x) = x^3 + 8x and g(x) = √(5x). This solution breaks down the function evaluation step by step and simplifies the result. Suitable for Grades 10-12.

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