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99 Percentile Qs Bank for JEE MainMathematicsFunctions

If f x = s i n x + c o s x and g x = x 2 - 1 , then g f x is invertible in the domain

Options

  1. A0 , π 2
  2. B- π 4 , π 4
  3. C- π 2 , π 2
  4. D0 , π

Correct answer

B. - π 4 , π 4

Step-by-step solution

Given, f x = s i n x + c o s x g x = x 2 - 1 g f x = f x 2 - 1 = s i n x + c o s x 2 - 1 = s i n 2 x But sin 2 x is invertible in a case when - π 2 ≤ 2 x ≤ π 2 ⇒ - π 4 ≤ x ≤ π 4

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