The expression in the image shows the following mathematical equation:

$f(-2) = -(-2)^2 - 1$

Now, let's evaluate this step by step:

1. Exponentiation: $(-2)^2$ means $(-2) \times (-2) = 4$.

   So the expression becomes: $f(-2) = -4 - 1$

2. Subtraction: $-4 - 1 = -5$.

Thus, the final value is:

$f(-2) = -5$

Would you like further clarification or details on this process?

Here are 5 related questions to explore:

1. What is the general form of the function $f(x) = -(x^2) - 1$?
2. How do different values of $x$ affect the output of this function?
3. What is the significance of squaring a negative number?
4. How does the function behave for positive and negative inputs?
5. Can we graph this function to understand its shape?

Tip: Always handle the order of operations carefully, especially with negative numbers and exponents.