The function is

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The function

f(x)=\begin{cases}\frac{\pi}{4}+\tan^{-1}x, & |x|\leq1\\\frac{1}{2}(|x|-1), & |x|>1\end{cases}

is (a) Both continuous and differentiable on

\mathbb{R}\setminus\{-1\}

(b) Both continuous and differentiable on

\mathbb{R}\setminus\{1\}

\mathbb{R}\setminus\{-1\}

and differentiable on

\mathbb{R}\setminus\{-1,1\}

(d) Continuous on

\mathbb{R}\setminus\{1\}

and differentiable on

\mathbb{R}\setminus\{-1,1\}