Home
Class 12
MATHS
If f(x)=(4x+x^(4))/(1+4x^(3))andg(x)=In ...

If `f(x)=(4x+x^(4))/(1+4x^(3))andg(x)=In ((1+x)/(1-x))`, then what is the value of `f^(@)g((e-1)/(e+1))` equal to?

A

2

B

1

C

0

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=(4x+x^(4))/(1+4x^(3)),g(x)=ln((1+x)/(1-x))`
`g((e-1)/(e+1))=ln((1+((e-1)/(e+1)))/(1-((e-1)/(e+1))))=ln((e+1+e-1)/(e+1-e+1))`
`=ln((2l)/(2))=lne=1`
`fog((e-1)/(e+1))=f(1)=(4(1)+(1)^(4))/(1+4(1)^(3))=(4+1)/(1+4)=(5)/(5)=1`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

If the function f (x)=-4e^((1-x)/(2))+1 +x+(x ^(2))/(2)+ (x ^(3))/(3) and g (x) =f ^(-1)(x), then the value of g'((-7)/(6)) equals :

If the function f (x)=- 4e^((1-x)/(2))+1+x+(x ^(2))/(2)+ (x ^(3))/(3) and g (x) =f ^(-1) (x), then the vlue of g'((-7)/(6)) equals to :

If f(x)=e^(g(x)) and g(x)=int_(2)^(x)(tdt)/(1+t^(4)), then find the value of f'(2)

If f(x)=log_(e)((1+x)/(1-x)),g(x)=(3x+x^(3))/(1+3x^(2))andgof(t)=g(f(t)) then what is g^(@)f((e-1)/(e+1)) equal to?

Let g(x) be differentiable function on R such f(x)=g(x)ln(4x^(3)-x)andg'((1)/(3))=-5 then the value of f' ((1)/(3)) is equal to

If the function _(x)f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x), then the value of g'(1) is

Q.if the function f(x)=x^(3)+(e^(x))/(2) and g(x)=f^(-1)(x), then find the value of g'(1)

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. Let g be the greatest integer function. Then the function f(x)=(g(x))^...

    Text Solution

    |

  2. Consider the following statements : Statement I : xgtsinx" for all...

    Text Solution

    |

  3. If f(x)=(4x+x^(4))/(1+4x^(3))andg(x)=In ((1+x)/(1-x)), then what is th...

    Text Solution

    |

  4. Which one of the following is correct in respect of the function f:RRt...

    Text Solution

    |

  5. Suppose f:RRtoRR^(+) is defined by f(x)=(x^(2))/(1+x^(2)). What is the...

    Text Solution

    |

  6. If f(x)=|x|+|x-1|, then which one of the following is correct?

    Text Solution

    |

  7. Conisder the function f(x)={{:(x^(2)ln|x|,xne0),(0,x=0):}. "What is" f...

    Text Solution

    |

  8. If f(x)=(x^(2)-9)/(x^(2)-2x-3),xne3 is continuous at x=3, then which o...

    Text Solution

    |

  9. If f:RRtoS defined by f(x)=4sinxx-3cosx+1 is onto, then what is S equa...

    Text Solution

    |

  10. For f to be a function, what is the domain of f, if f(x)=(1)/(sqrt(|x|...

    Text Solution

    |

  11. What is lim(x to 0) (tanx)/(sin2x) equal to?

    Text Solution

    |

  12. What is lim(h to 0) (sqrt(2x+3h)-sqrt2x)/(2h) equal to?

    Text Solution

    |

  13. If f(x) is an even function, then write whether f^(prime)(x) is eve...

    Text Solution

    |

  14. Let A=(X"inR:-1lexle1)andS be the subset of AxxB, defined by S=[(x,y)i...

    Text Solution

    |

  15. If f(x)=sqrt(x-1)/(x-4) defines a function of R, then what is its doma...

    Text Solution

    |

  16. Consider the function f(x)={{:((sin2x)/(5x),if ,xne0),((2)/(15),if,x...

    Text Solution

    |

  17. For the function f(x)=|x-3|, which of the following is not correct?

    Text Solution

    |

  18. If the function f9x)=(2x-sin^(-1)x)/(2x+tan^(-1)x) is continuous at ea...

    Text Solution

    |

  19. If f(x )=sqrt(25-x^(2)), then what is lim(x to 1) (f(x)-f(1))/(x-1) eq...

    Text Solution

    |

  20. What is lim(thetato0)(sqrt(1-costheta))/(theta) equal to?

    Text Solution

    |