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F(x) = | x |

= x , for x ≥ 0

= - x , for x ≤ 0

f( Log x) = | Log x |

= Log x , for 1 < x ≤ ∞

= 0 for x = 1

= - Log x for 0 < x < 1

= undefined for x ≤ 0

The function f (Log x) exists in (0, ∞). It is continuous at all points. Let us find the derivative from left side and right side of x = 1.

At x = 1, the derivative from right side is 1 and from left side is -1. So there is no derivative defined for x = 1. Otherwise, it is defined as:

So the answer is :

it is 1/x * |x-1|/(x-1) defined for x > 0

So the answer is none of the given options.

= x , for x ≥ 0

= - x , for x ≤ 0

f( Log x) = | Log x |

= Log x , for 1 < x ≤ ∞

= 0 for x = 1

= - Log x for 0 < x < 1

= undefined for x ≤ 0

The function f (Log x) exists in (0, ∞). It is continuous at all points. Let us find the derivative from left side and right side of x = 1.

__Right side Differential coefficient for x > 1:____Left side differential coefficient for 0< x < 1 :__At x = 1, the derivative from right side is 1 and from left side is -1. So there is no derivative defined for x = 1. Otherwise, it is defined as:

*Differential coefficient of f (Log x) :**1/x for x > 1**undefined for x = 1**-1/x for 0 < x < 1**undefined for x <= 0*So the answer is :

it is 1/x * |x-1|/(x-1) defined for x > 0

So the answer is none of the given options.