https://file.aiquickdraw.com/mathbot/file/17318732120926pdq62hp.jpg

The given function appears to be:

\[
f(x) = \frac{x \sqrt{x+1}}{x+1}
\]

Would you like me to:

1. Analyze the domain of \( f(x) \)?
2. Differentiate \( f(x) \) to find critical points or extrema?
3. Simplify the function and analyze its behavior?
4. Discuss asymptotic behavior or limits at certain points?
5. Provide a plot of \( f(x) \) over a specified interval?

Let me know how you'd like to proceed!

**Tip:** Always check the domain of a function before analyzing other properties like derivatives or integrals.

Analyze the function f(x) = \( \frac{x \sqrt{x+1}}{x+1} \) as shown in the provided image. The goal might be to find its domain, critical points, or behavior.

Explore the function f(x) = x sqrt(x+1) / (x+1), including its domain, derivative analysis for critical points, and overall behavior. Suitable for advanced high school or early college-level students.

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