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 let `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`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

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

Let f be a non-negative function defined on the interval [0,1] . If int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n d \ f(0)=0 , then

Let f:R ->(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then find f(x) ?

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

Let agt1 be a real number and f(x)=log_(a)x^(2)" for "xgt 0. If f^(-1) is the inverse function of f and b and c are real numbers then f^(-1)(b+c) is equal to

If the function f be defined by f(x) =(2x +1)/(1-3x) , then f ^(-1) (x) is-

Let f:[1,oo) → [2, ∞) 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

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Prove that the value of the integral, int(0)^(2a)(f(x))/(f(x)+f(2a-x)...

    Text Solution

    |

  2. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

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

    Text Solution

    |

  4. int(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

    Text Solution

    |

  5. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

    Text Solution

    |

  6. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  7. (lim)(n to oo)n/(2^n)int0^2x^n dx equals

    Text Solution

    |

  8. Let f:[0,oo) to R be a continuous strictly increasing function, such t...

    Text Solution

    |

  9. A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint0^...

    Text Solution

    |

  10. L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int(1/4)^(3/4)f(f(x...

    Text Solution

    |

  11. Evaluate: int0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest inte...

    Text Solution

    |

  12. Consider the polynomial f(x)=a x^2+b x+c dot If f(0)=0,f(2)=2, then th...

    Text Solution

    |

  13. Find the points at which the function f given by f(x)=x^3-3x has local...

    Text Solution

    |

  14. STATEMENT 1: If f(x) is continuous on [a , b] , then there exists a po...

    Text Solution

    |

  15. Each question contains statements given in two columns which have to b...

    Text Solution

    |

  16. The value of the definite integral, int0^(pi/2) (sin5x)/sinx dx is

    Text Solution

    |

  17. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, n in I (a) pi/2 ...

    Text Solution

    |

  18. IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n...

    Text Solution

    |

  19. If In=int0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ...

    Text Solution

    |

  20. int0^1(tan^(-1)x)/x dx is equals to (a) int0^(pi/2)(sinx)/x dx (b)...

    Text Solution

    |