$\displaystyle f(x) = 2(x - 1)^2 - 3$

$\displaystyle f(x) = (2x - 2)^2 - 3$

$\displaystyle (2x - 2)^2 = x + 3$

$\displaystyle 2x - 2 = \pm \sqrt{x + 3}$

$\displaystyle 2x = \pm \sqrt{\frac{x + 3}{2}}$

$\displaystyle x = \pm \sqrt{\frac{x + 3}{2}} + 2$

$\displaystyle f^-(x) = \pm \sqrt{\frac{x + 3}{2}} + 2$

That's how I solved it, but my textbook answer is

$\displaystyle f^-(x) = 1 \pm \sqrt{\frac{x + 3}{2}}$

Where was my error?