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  4. The domain of the derivative of the function f(x) = begincases tan-1 x textif |x| le 1 (1/2) ( |x| - 1) textif |x | > 1 endcases is

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Q. The domain of the derivative of the function $f(x) = \begin{cases} \tan^{-1} x & \quad \text{if } |x| \le 1 \\ \frac{1}{2} ( |x| - 1) & \quad \text{if } |x | > 1 \end{cases} $ is

Limits and Derivatives

Solution:

Correct answer is (d) $R \sim \{- 1 , 1 \}$