Find the set of value of x for which f(x) = tan-1 x is increasing in

  1. (-∞,0)
  2. (-∞,∞)
  3. (0,∞)
  4. [0,∞)

Answer (Detailed Solution Below)

Option 2 : (-∞,∞)
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Detailed Solution

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Concept:

  • If f′(x) > 0 then the function is said to be increasing.
  • If f′(x) < 0 then the function is said to be decreasing.

Calculation:

Given:

f(x) = tan-1 x

Differentiating with respect to x, we get

As we know that, x2 > 0 for x ∈ R

⇒ 1 + x2 > 0 for x ∈ R

So, 1 + x2 gives positive values for x ∈ R

Therefore, f’(x) > 0 for x ∈ R

Hence f(x) is increasing in x ∈ R or x ∈ (-∞,∞)

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