To reflect the function \( f(x) = x^2 - 1 \) over the y-axis, we replace \( x \) with \( -x \) in the function.
Thus, the reflection is:
\[ g(x) = f(-x) = (-x)^2 - 1 \]
Calculating this gives:
\[ g(x) = x^2 - 1 \]
So the correct choice is:
C. g(x) = x^2 - 1