Home
Class 12
MATHS
Let f be a real-valued function defined ...

Let `f` be a real-valued function defined on the inverval `(-1,1)` such that `e^(-x)f(x)=2+int_0^xsqrt(t^4+1)dt ,` for all, `x in (-1,1)and f^(-1)` be the inverse function of `fdot` Then `(f^(-1))^'(2)` is equal to

A

1

B

`1//3`

C

`1//2`

D

`1//e`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise FUNCTION EXERCISE 8:Questions Asked in Previous 10 Years Exams|2 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f be a real valued function defined on the interval (0,oo) by f(x)=In x+int_(0)^(x)sqrt(1+sint)dt . Then which of the following statement (s) is (are) true?

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The value of f(10) is equal to

The function f(x)= int_0^x sqrt(1-t^4)dt is such that:

If g is te inverse of a function f and f'(x) = 1/(1+x^5) then g'(x) is equal to

Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If g(2)=a then g'(2) is equal to

Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in (0,oo) and f(1) ne 1. Then

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

Let f(x) is a real valued function defined by f(x)=x^(2)+x^(2) int_(-1)^(1) tf(t) dt+x^(3) int_(-1)^(1)f(t) dt then which of the following hold (s) good?

Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

    Text Solution

    |

  2. Let f(x)=x^2a n dg(x)=sinx for all x in R Then the set of all x satis...

    Text Solution

    |

  3. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  6. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

    Text Solution

    |

  7. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g(f(x)) is invertible in the do...

    Text Solution

    |

  8. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  9. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (a) (...

    Text Solution

    |

  10. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  11. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  12. Let E={1,2,3,4} and F={1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  13. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  14. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  15. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

    Text Solution

    |

  16. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

    Text Solution

    |

  17. Let f(x)=(alphax)/((x+1)),x!=-1. The for what value of alpha is f(f(x)...

    Text Solution

    |

  18. Text Solution

    |

  19. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |

  20. Let f(theta)=sintheta(sintheta+sin3theta)dot Then f(theta)i s

    Text Solution

    |