The question in your image asks: "What value should be assigned to $f(2)$ to make the extended function continuous at $x = 2$?"

From the right-hand side, it looks like the function is piecewise, with different expressions depending on the value of $x$. To make the function continuous at $x = 2$, the left-hand limit and right-hand limit as $x$ approaches 2 must be equal, and the function value at $x = 2$ must match these limits.

Could you provide a closer view or describe the piecewise function? This will help in determining the appropriate value for $f(2)$ to ensure continuity.

Let me know if you'd like me to elaborate further or explain any concepts!

Here are some relative questions to consider:

1. What is the definition of continuity for a function at a point?
2. How do you calculate the left-hand and right-hand limits of a function?
3. What are piecewise functions and how do they affect continuity?
4. Can a function be continuous if it has a hole or jump at a specific point?
5. How do you use limits to determine if a function is continuous?

Tip: Continuity at a point implies that the function's limit from both sides and the function's value at that point must all be equal.