The function \(f\left(x\right)=\left{\begin{matrix}\frac{\pi }{4}+{\tan }^{-1}x,\left|x\right|\leq 1 \\ \frac{1}{2}\left…

both continuous and differentiable on \( \mathrm{R}-\{-1\} \).

both continuous and differentiable on \( \mathrm{R}-\{1\} \).

continuous on \( R-\{-1\} \) and differentiable on \( \mathrm{R}-\{-1,1\} \).

continuous on \( \mathrm{R}-\{1\} \) and differentiable on \( \mathrm{R}-\{-1,1\} \)