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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

If y = g ( x ) is a curve which is obtained by the reflection of y =f( x )= e ^ x - e ^ - x 2 about the line y = x , then which of the following is/are true -

Options

  1. Ay=g(x) has exactly one tangent parallel to x -axis
  2. By=g(x) has no tangent parallel to x -axis
  3. CThe tangent to y=g(x) at (0,0) is y=x
  4. Dg(x) has no extremum

Correct answer

D. g(x) has no extremum

Step-by-step solution

Clearly g ( x )= f ⁻¹( x )= ( x + 1+ x ^2 ) array ll & g ^ ( x )= 1 1+ x ^2 0 x R & g ^ ( x ) 0 x R array So no tangent is parallel to x axis. g(x) has no extremum. At (0,0) g^ (0)=1 So equation of tangent is y = x

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