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99 Percentile Qs Bank for JEE MainMathematicsContinuity and Differentiability

If f(x)= ⁻¹ ( 2 x 1+x² ) , then f(x) is differentiable on

Options

  1. A[-1,1]
  2. BR- -1,1
  3. CR-(-1,1)
  4. DNone of these

Correct answer

B. R- -1,1

Step-by-step solution

Given, f(x)= ⁻¹ ( 2 x 1+x² ) On differentiating w.r.t. x , we get aligned f^ (x) &= 1 1- ( 2 x 1+x² )² d d x ( 2 x 1+x² ) &= 1+x² (1-x² )² 2 (1-x² ) (1+x² )² aligned = 2 1+x² 1-x² |1-x² | = array l 2 1+x² , if |x| 1 array . f^ (x) does not exist for |x|=1, i e, x= 1 Hence, f(x) is differentiable on R- -1,1 .

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