We are given that the function $f(x) = x^2 - 1$ is reflected over the y-axis, and we need to determine the equation for $g(x)$, the reflected function.

Reflection over the y-axis:

To reflect a function over the y-axis, we replace $x$ with $-x$ in the function. This means that the function $f(x)$ will become:

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

Since $(-x)^2 = x^2$, the equation simplifies to:

$g(x) = x^2 - 1$

Thus, the reflected function is $g(x) = x^2 - 1$.

Conclusion:

The correct equation is $g(x) = x^2 - 1$, which matches the fourth option in the given choices.

Let me know if you'd like further details or have questions.

Here are 5 related questions to expand your understanding:

1. How do you reflect a function over the x-axis?
2. What is the general rule for reflecting functions over the line $y = x$?
3. How would you reflect the function $f(x) = x^2 - 1$ over the x-axis?
4. What would happen if you shifted the function $f(x)$ by 2 units to the right?
5. How does the graph of $g(x) = x^2 - 1$ compare to $g(x) = -x^2 - 1$?

Tip: Whenever reflecting a function over the y-axis, remember to substitute $x$ with $-x$.