To reflect the function \( f(x) = x^2 - 1 \) over the y-axis, we need to replace \( x \) with \( -x \).
When we do that, we get:
\[ g(x) = f(-x) = (-x)^2 - 1 = x^2 - 1 \]
So, the reflection of \( f(x) \) over the y-axis gives us:
\[ g(x) = x^2 - 1 \]
Therefore, the correct equation for \( g(x) \) is:
\[ g(x) = x^2 - 1 \]
From the provided options, the correct choice is:
g(x) = x² - 1.