Ah, I see now! You are defining the function \( f(x) \) as:

\[
f(x) = \sqrt[7]{8x} + 5
\]

This means that \( f(x) \) consists of two parts:

1. \( \sqrt[7]{8x} \): The 7th root of \( 8x \).
2. \( + 5 \): A constant that is added after computing the 7th root.

### Explanation

- **7th Root**: The 7th root of a number \( y \) is the value that, when raised to the power of 7, gives \( y \). So, \( \sqrt[7]{8x} \) represents the number that, when raised to the 7th power, equals \( 8x \).
  
- **Addition**: After computing the 7th root, you add 5 to the result.

### Example Evaluation

For example, if you wanted to evaluate \( f(x) \) at \( x = 1 \), you would do the following:

\[
f(1) = \sqrt[7]{8(1)} + 5 = \sqrt[7]{8} + 5
\]

The 7th root of 8 is approximately 1.1547, so:

\[
f(1) \approx 1.1547 + 5 = 6.1547
\]

### Do you need more help with:
- Evaluating the function for different values of \( x \)?
- Understanding its graph?
- Finding its derivative?

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Here are 5 related questions:
1. How does the function \( f(x) = \sqrt[7]{8x} + 5 \) behave as \( x \) increases?
2. What is the domain of \( f(x) \)?
3. What is the derivative of \( f(x) \)?
4. What happens to \( f(x) \) as \( x \) approaches 0?
5. How would you graph this function?

**Tip:** When working with roots, odd roots (like the 7th root) are defined for both positive and negative values of the argument, so the domain of the function can include negative \( x \).

Explore the function f(x) = ∛8x + 5, which involves computing the seventh root of 8x and adding 5. Learn how to evaluate this function for different values of x and understand its behavior. Suitable for advanced high school students and those interested in mathematical functions.

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