To reflect the function \( f(x) = x^2 - 1 \) over the y-axis, we replace \( x \) with \( -x \) in the function.
So, the equation for the reflected function \( g(x) \) is:
\[ g(x) = f(-x) = (-x)^2 - 1 \]
Now, simplifying this gives:
\[ g(x) = x^2 - 1 \]
Thus, the equation that correctly identifies \( g(x) \) after reflecting \( f(x) \) over the y-axis is:
\[ g(x) = x^2 - 1 \]
This means that reflecting \( f(x) \) over the y-axis does not change the function since it is an even function.