How does this probability transformation question simplify? Suppose that X is unif(-1,1) and Y= X^2. Then $f_y(y) = f_x(-\sqrt{y}) *|-1/(2\sqrt{y}) | + f_x(\sqrt{y})*|1/(2\sqrt{y}) | $

this makes sense to me, but then they simplify it to $1/(2\sqrt{y})$

which to me doesn't make sense, wouldn't it be $1/(\sqrt{y})$ since both $f_x(+/- \sqrt{y})$ become 1, they uniform so the pdf is 1/(b-a), which is in both cases 1?
The uniform is over the range -1 to 1, so the $f_x(x) = \dfrac{1}{2}$, not 1.
The uniform is over the range -1 to 1, so the $f_x(x) = \dfrac{1}{2}$, not 1.