https://file.aiquickdraw.com/mathbot/file/17295204022129ejgx6xx.jpg

The function provided in the image is:

\[
g(x) = \frac{\sec(x) - \frac{1}{x}}{\sin(x)}
\]

Would you like to find the derivative of \(g(x)\), evaluate it for a specific value, or simplify the expression? Let me know how you'd like to proceed.

Here are five potential follow-up questions:
1. Would you like to find the derivative \(g'(x)\) using the quotient rule?
2. Are there specific values of \(x\) you'd like to evaluate for \(g(x)\)?
3. Should we check if the function has any asymptotes or discontinuities?
4. Would you like to analyze the behavior of \(g(x)\) as \(x\) approaches zero?
5. Are there any particular points of interest you'd like to explore for \(g(x)\), such as critical points?

**Tip:** When working with trigonometric functions and rational expressions, always be mindful of points where the function might be undefined, like when denominators equal zero.

Find the behavior or properties of the function g(x) = (sec(x) - 1/x) / sin(x).

Explore the properties of the trigonometric function g(x) = (sec(x) - 1/x) / sin(x). Learn about its derivative using the quotient rule and investigate its behavior at critical points such as x approaching 0. Suitable for advanced high school or early college students.

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