## Thomas' Calculus 13th Edition

$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \$ $x^{2}-1\leq y\leq x^{2}+1$ $\}$
The domain of f depends on the domain of $\cos^{-1}t$, which is the range of $\cos t,$ which is $[-1,1].$ So f will be defined only for those $(x,y)$ for which $1\leq y-x^{2}\leq 1,$ $x^{2}-1\leq y\leq x^{2}+1$ This is the region between the curves $\left\{\begin{array}{l} y=x^{2}-1\\ y=x^{2}+1 \end{array}\right..$ The curves themselves are included, so they are graphed with a solid line. Domain: $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \$ $x^{2}-1\leq y\leq x^{2}+1$ $\}$