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 $x$.