Home
Class 12
MATHS
Let f(x)=int(0)^(x)(dt)/(sqrt(1+t^(3))) ...

Let `f(x)=int_(0)^(x)(dt)/(sqrt(1+t^(3)))` and `g(x)` be the inverse of `f(x)`. Then the value of `4 (g''(x))/(g(x)^(2))` is________.

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=int_2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Then the value of g'(0)

Let f(x)=int_2^x (dt)/sqrt(1+t^4) and g be the inverse of f . Then, the value of g'(0) is

Let f(x) = int_(0)^(x)(dt)/(sqrt(1+t^(2))) and g(x) be the inverse of f(x) , then which one of the following holds good ? (A) 2g'' = g^(2) (B) 2g'' = g^(2) (C) 3g'' = 2g^(2) (D) 3g'' = g^(2)

Let f(x)=-4.sqrt(e^(1-x))+1+x+(x^(2))/(2)+(x^(3))/(3) . If g(x) is inverse of f(x) then the value of (1)/(g^(')(-(7)/(6))) is

Let f (x) = x^(3)+ 4x ^(2)+ 6x and g (x) be inverse then the vlaue of g' (-4):

If f(x)=x^(3)+3x+1 and g(x) is the inverse function of f(x), then the value of g'(5) is equal to

If f (x) =int _(0)^(g(x))(dt)/(sqrt(1+t ^(3))),g (x) = int _(0)^(cos x ) (1+ sint ) ^(2) dt, then the value of f'((pi)/(2)) is equal to:

If f (x) =int _(0)^(g(x))(dt)/(sqrt(1+t ^(3))),g (x) = int _(0)^(cos x ) (1+ sint ) ^(2) dt, then the value of f'((pi)/(2)) is equal to:

If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the value of (d)/(dx)((g(x))/(g(g(x)))) at x = 4 equals

If f(x) = x^(2) and g(x) = (1)/(x^(3)) . Then the value of (f(x)+g(x))/(f(-x)-g(-x)) at x = 2 is

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If f : R rarr R is a function defined by f(x) = [x] cos ((2x -1)/(2))p...

    Text Solution

    |

  2. Evaluate the determinants(i) |3-1-2 0 0-1 3-5 0| (ii) |3-4 5 1 1-2 2 ...

    Text Solution

    |

  3. Let f(x)=int(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x...

    Text Solution

    |

  4. Evaluate the determinants |[3,-1,-2],[0,0,-1],[3,-5,0]|

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. Evaluate the determinants |[3,-1,-2],[0,0,-1],[3,-5,0]|

    Text Solution

    |

  7. If ain[-20, 0], find the probability that the graph of the function y=...

    Text Solution

    |

  8. Evaluate the determinants in|2 4-5-1|

    Text Solution

    |

  9. The number of values of k for which the system of equations (k+1)x+8y=...

    Text Solution

    |

  10. Find the value of C D in terms of x , in the adjoining figure, where...

    Text Solution

    |

  11. In a city no two persons have identical set of teeth and there is n...

    Text Solution

    |

  12. Solve the following inequalities ((x-1)(x+2)(x-3))/((x+1)(x+2)(x+3))>1

    Text Solution

    |

  13. Let f(x ,y)=x y^2 if xa n dy satisfy x^2+y^2=9 then the minimum value ...

    Text Solution

    |

  14. Solve (i)" "(x-1)/(x)-(x-1)/(x-1)lt2" "(ii)" "(x^(2)+4x+4)/(2x^(2)-x-...

    Text Solution

    |

  15. If a,b,c are distinct odd integers and omega is non real cube real of ...

    Text Solution

    |

  16. If f(x)=x^4-2x^3+3x^2-a x+b is a polynomial such that when it is divid...

    Text Solution

    |

  17. The range of the function f(x)=(1+sec^(-)x)(1+cos^(-1)x) is

    Text Solution

    |

  18. The expression \(root(3)root(6){a^{9}))^4 \(root(6)root(3){a^{9}))^4...

    Text Solution

    |

  19. The real value of k for which the system of equation 2k x-2y+3z=0, x+k...

    Text Solution

    |

  20. In the figure, if A B=A C ,/B A D=30^0 and A E=A D , then x is equal t...

    Text Solution

    |