To reflect the function \( f(x) = x^2 - 1 \) over the y-axis, we need to replace \( x \) with \( -x \) in the equation.
So, we have:
\[ g(x) = f(-x) = (-x)^2 - 1 \]
Calculating this gives:
\[ g(x) = x^2 - 1 \]
Now, we compare this with the options provided:
a. \( g(x) = x^2 + 1 \)
b. \( g(x) = x^2 - 1 \)
c. \( g(x) = -x^2 + 1 \)
d. \( g(x) = x^2 - 2 \)
The correct choice that matches our derived equation \( g(x) = x^2 - 1 \) is:
b. \( g(x) = x^2 - 1 \).