For $x \in \,R,\,\,f\left( x \right) = \left| {\log 2 - \sin x} \right|\,\,$ and $\,\,g\left( x \right) = f\left( {f\left( x \right)} \right),\,\,$ then :

Question

For $x \in \,R,\,\,f\left( x \right) = \left| {\log 2 - \sin x} \right|\,\,$

and $\,\,g\left( x \right) = f\left( {f\left( x \right)} \right),\,\,$ then :

$g$ is not differentiable at $x=0$

$g'\left( 0 \right) = \cos \left( {\log 2} \right)$

$g'\left( 0 \right) = - \cos \left( {\log 2} \right)$

$g$ is differentiable at $x=0$ and $g'\left( 0 \right) = - \sin \left( {\log 2} \right)$

Solution

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