The function f(x)= cases 4 + ^ -1 x,&|x| 1 1 2 (|x|-1),&|x|>1 cases is

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

The function f(x)={π4+tan⁡−1x,∣x∣≤112(∣x∣−1),∣x∣>1f(x)=\begin{cases}\frac{\pi}{4}+\tan^{-1}x,&|x|\le1\\\frac{1}{2}(|x|-1),&|x|>1\end{cases} is (a) both continuous and differentiable on R∖{−1}\mathbb{R}\setminus\{-1\} (b) both continuous and differentiable on R∖{1}\mathbb{R}\setminus\{1\} (c) continuous on R∖{−1}\mathbb{R}\setminus\{-1\} and differentiable on R∖{−1,1}\mathbb{R}\setminus\{-1,1\} (d) continuous on R∖{1}\mathbb{R}\setminus\{1\} and differentiable on R∖{−1,1}\mathbb{R}\setminus\{-1,1\}

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