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The function given is:

\[
f(x) = \sqrt[3]{5x - 7} + 10
\]

This function is a **cube root** function because the main operation performed on \( x \) is a cube root transformation. The function can be expressed in the form \( f(x) = \sqrt[3]{g(x)} + c \), where \( g(x) = 5x - 7 \) is a linear expression inside the cube root and \( c = 10 \) is a constant added to it.

Thus, the correct answer is:

**Cube Root**

Would you like to go into more details, or do you have any additional questions?

Here are 5 related questions for deeper understanding:

1. What are the general properties of cube root functions?
2. How does adding a constant like 10 affect the graph of a cube root function?
3. How would the graph of \( f(x) \) change if the linear term inside the cube root was different?
4. What is the domain and range of this cube root function?
5. How can you determine the inverse of a cube root function?

**Tip**: Remember that cube root functions, unlike square root functions, are defined for all real numbers.

What type of function is f(x) = ³√(5x - 7) + 10?

Explore how to identify and understand cube root functions with the example f(x) = ³√(5x - 7) + 10. This problem introduces key concepts in algebra, including cube root transformations, domain, and range properties. Suitable for students in Grades 10-12.

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