To reflect the function \( f(x) = x^2 - 1 \) over the y-axis, we replace \( x \) with \( -x \) in the equation. The reflected function \( g(x) \) is given by:
\[ g(x) = f(-x) = (-x)^2 - 1 \]
Since \( (-x)^2 = x^2 \), we have:
\[ g(x) = x^2 - 1 \]
Therefore, the correct choice for \( g(x) \) after reflecting over the y-axis is:
\[ g(x) = x^2 - 1 \]
From your options, it seems like the correct option might not have been clearly listed, but if one of them corresponds to \( g(x) = x^2 - 1 \), that would be the correct reflection of the function.