This image contains a mathematical problem written in Greek. Let me translate and interpret the content for you:

Given:

• $f: \mathbb{R} \rightarrow \mathbb{R}$
• $f(x) = \sqrt{x^2 + 1} - 6x, \ \forall x \in \mathbb{R}$

The task is to determine the behavior (probably asking for limits, continuity, or the derivative) of the function $f$.

Would you like me to solve for the function's derivative, or perhaps analyze its behavior such as limits, continuity, or maximum/minimum points?

Feel free to clarify or ask for any further details. Here are some possible follow-up questions to consider:

1. What is the derivative of $f(x)$?
2. What is the limit of $f(x)$ as $x \to \infty$?
3. What are the critical points of $f(x)$?
4. How do you determine the concavity of $f(x)$?
5. How does the function behave at specific points like $x = 0$ or $x = 1$?

Tip: When dealing with square roots and algebraic functions, check for possible restrictions in the domain to ensure the function behaves properly over all real numbers.