The set of all points, where the function  is differentiable, is

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NDA (Held On: 10 Sept 2017) Maths Previous Year paper
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  1. (0, ∞)
  2. (-∞, ∞) 
  3. (-∞, 0) ∪ (0, ∞) 
  4. (-1, ∞)

Answer (Detailed Solution Below)

Option 3 : (-∞, 0) ∪ (0, ∞) 
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Detailed Solution

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Concept:

  • A function is differentiable at a point when there's a defined derivative at that point.
  • Denominator should not be zero
  • Chain Rule:

 

Calculation:

Given:

      

Now, at x = 0, f’(x) = 0/0

So, f’(x) is defined for all values of x except x = 0

⇒ f(x) is differentiable on (-∞, 0) ∪ (0, ∞)

Hence, option (3) is correct.

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