The domain of the derivative of the function: `f(x)={{:(,tan^(-1)x,|x| le1),(,(1)/(2)(|x|-1),|x|gt1):}`

The domain of the derivative of the function f(x) = {(tan^(-1)x, |x|le1),(1/2(|x|-1), |x|gt1):} is

The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|lt=1), (1/2(|x|-1),if|x|>1):}

The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|lt=1), (1/2(|x|-1),if|x|>1 ):}

The function f(x)={{:((pi)/(4)+tan^(-1)x",",|x|le1),((1)/(2)(|x|-1)",",|x|gt1):} is :

The domain of the derivation of the functions f(x) = {{:(tan^(_1) x", if " |x|le1),(" is"),(1/2(|x|-1)", if "|x| gt 1):}

The domain set of the function f(x) = tan^(-1) x -cot ^(-1) x + cos ^(-1) ( 2-x) is

The domain set of the function f(x) = tan^(-1) x -cot ^(-1) x + cos ^(-1) ( 2-x) is

Discuss the applicability of Rolle's theorem for the function f(x)={{:(x^(2)-4",",x le1),(5x-8"," , x gt1):}