Home
Class 12
MATHS
Let f : R ^(+) to R defined as f (x)= e ...

Let `f : R ^(+) to R` defined as `f (x)= e ^(x) + `ln x and `g = f ^(-1)` then correct statement (s) is/are:

A

`g''(e)=(1-e)/((1+e)^(3))`

B

`g ''(e) (e-1)/((1+e)^(3))`

C

`g '(e) =e+1`

D

`g '(e) =(1)/(e+1)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|29 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|3 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|22 Videos
  • COMPOUND ANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VK JAISWAL ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

if f:RtoR is defined as f(x)=e^(|x|)-e^(-x) then the correct statements(s) is/are

Let f:Rto R be a functino defined by f (x) = e ^(x) -e ^(-x), then f^(-1)(x)=

Let f:R to R defined by f(x)=x^(2)+1, forall x in R . Choose the correct answer

If f: R to R be defined by f(x) =(1)/(x), AA x in R. Then , f is

Let f: (e, oo) -> R be defined by f(x) =ln(ln(In x)) , then

Let f: R->R^+ be defined by f(x)=a^x ,\ a >0 and a!=1 . Write f^(-1)(x) .

For x in R, f(x) = | log 2- sin x| and g(x) = f(f(x)) , then

f:R to R is a function defined by f(x)= 10x -7, if g=f^(-1) then g(x)=

Let f: R->R be defined by f(x)=x^4 , write f^(-1)(1) .

Let f:R to R be the function defined by f(x)=2x-3, AA x in R. Write f^(-1).

VK JAISWAL ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. If f (x) be a differentiable function satisfying f (y) f ((x)/(y))=f (...

    Text Solution

    |

  2. Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...

    Text Solution

    |

  3. let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...

    Text Solution

    |

  4. Let y=e^x s in x^3+(t a n x)^xdotF in d(dy)/(dx)dot

    Text Solution

    |

  5. Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x...

    Text Solution

    |

  6. Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...

    Text Solution

    |

  7. If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),...

    Text Solution

    |

  8. If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) ...

    Text Solution

    |

  9. Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ...

    Text Solution

    |

  10. If f(x)={|x|-3 x < 1|x-2|+a x >= 1 & g(x)={2-|x| x < 2 sgn(x)-b x >= 2...

    Text Solution

    |

  11. Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln...

    Text Solution

    |

  12. f (x) is differentiable function satisfying the relationship f ^(2) (x...

    Text Solution

    |

  13. The function f (x)=[sqrt(1-sqrt(1-x ^(2)))],(where [.] denotes greates...

    Text Solution

    |

  14. A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...

    Text Solution

    |

  15. The points of discontinuities of f (x)= [(6x)/(pi)]cos [(3x)/(pi)]"in"...

    Text Solution

    |

  16. Check the continuity of f(x) = {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+...

    Text Solution

    |

  17. If x=phi (t), y=psi(t), then (d ^(2)y)/(dx ^(2))=

    Text Solution

    |

  18. f (x)=[x] and g (x)= {{:( 0"," , x in I ),( x ^(2)"," , cancel(in)I)...

    Text Solution

    |

  19. Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) th...

    Text Solution

    |

  20. Let f (x)=[{:((3x-x ^(2))/(2),,, x lt 2),([x-1],,, 2 le x lt 3),( x ^(...

    Text Solution

    |