The domain of the derivative of the function $$f(x)=$$$$tan$$−$$1$$⁡x if |x|≤$$112($$|x|−$$1)$$ if |x|$$1$$

Question

The domain of the derivative of the function $$f(x)=$$$$tan$$−$$1$$⁡x     if |x|≤$$112($$|x|−$$1)$$ if |x|>$$1$$

Infinity Learn · Accepted Answer

$$f(x)=11+x2$$,  if x<$$1$$  and is will defined.              $$f(x)=12$$,  if x>$$1$$              $$=$$ −$$12$$,  if x<−$$1$$.Right derivative at $$x=1$$ is x→$$1lim12=12Left$$ derivative at $$x=1$$ is x→$$1lim11+x2=12Hence$$,  $$f(x)$$ at $$x=1$$ is $$12$$.                   $$f(x)$$ at $$x=$$−$$1$$ does not exist∴                $$f(x)$$ is well defined at all points except −$$1$$.Hence (3) is the correct answer.

$The domain of the derivative of the function f (x) = \{\begin{cases} \tan^{- 1} x if | x | \leq 1 \\ \frac{1}{2} (| x | - 1) if | x | > 1 \end{cases}$

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The domain of the derivative of the function f(x)=tan−1⁡x if |x|≤112(|x|−1) if |x|>1

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$The domain of the derivative of the function f (x) = \{\begin{cases} \tan^{- 1} x if | x | \leq 1 \\ \frac{1}{2} (| x | - 1) if | x | > 1 \end{cases}$