Solve {l}{ygeqx^2-2x-1}{yleqx+a}

$$\left\{ \begin{array} { l } { y \geq x ^ { 2 } - 2 x - 1 } \\ { y \leq x + a } \end{array} \right.$$

Solve for x

$$\left\{\begin{matrix}x=1\text{, }&y\geq -2\text{ and }y\leq a+1\\x\in \begin{bmatrix}-\sqrt{y+2}+1,\sqrt{y+2}+1\end{bmatrix}\text{, }&\left(y<a+1\text{ and }y\leq a-\frac{\sqrt{4a+13}}{2}+\frac{3}{2}\text{ and }y>-2\right)\text{ or }\left(y<a+1\text{ and }a\leq -\frac{13}{4}\text{ and }y>-2\right)\\x=\sqrt{y+2}+1\text{, }&a=y-\sqrt{y+2}-1\text{ and }y>-2\\x\in \begin{bmatrix}y-a,\sqrt{y+2}+1\end{bmatrix}\text{, }&\left(y\leq a+1\text{ and }a<-\frac{13}{4}\text{ and }y>-2\right)\text{ or }\left(y=a+1\text{ and }a>-3\right)\text{ or }\left(y<a+\frac{\sqrt{4a+13}}{2}+\frac{3}{2}\text{ and }y>a-\frac{\sqrt{4a+13}}{2}+\frac{3}{2}\text{ and }a>-\frac{13}{4}\text{ and }y>-2\right)\end{matrix}\right.$$

Solve for y

$$y\in \begin{bmatrix}x^{2}-2x-1,x+a\end{bmatrix}\text{, }a\geq x^{2}-3x-1$$