https://file.aiquickdraw.com/mathbot/file/1726799991329oueoqi1l.jpg

The equation in the image is:

\[
h(x) = 4f(x) + \frac{g(x)}{7}
\]

This equation represents a function \( h(x) \), which is defined as a linear combination of another function \( f(x) \) and a scaled version of a function \( g(x) \). Specifically:

- \( h(x) \) is a new function dependent on both \( f(x) \) and \( g(x) \).
- \( f(x) \) is multiplied by 4.
- \( g(x) \) is divided by 7, meaning it's scaled down by a factor of 7.

Would you like to solve for \( h(x) \) given \( f(x) \) and \( g(x) \), or do you need further details on how this equation works?

Here are 5 related questions:
1. What are the forms of \( f(x) \) and \( g(x) \)?
2. How do you find the derivative of \( h(x) \) given \( f(x) \) and \( g(x) \)?
3. How does scaling functions by constants affect their graphs?
4. What happens if \( f(x) \) or \( g(x) \) are specific functions, like polynomials or exponentials?
5. Can we interpret this equation in terms of a real-world problem?

**Tip:** In composite or combined functions, consider how changes in one component, like scaling or shifts, affect the entire function when graphing or calculating.

This problem explores the function h(x) = 4f(x) + g(x)/7, demonstrating how functions can be combined linearly and scaled. Learn how constants affect function scaling and how to interpret the equation h(x) as a function of both f(x) and g(x). Suitable for students in Grades 9-12.

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