Home
Class 12
MATHS
If f be a function satisfying f(x+y)=f(x...

If f be a function satisfying `f(x+y)=f(x)+f(y),AAx,yinR`. If f(1) = k, then f(n), `n in N` is equal to

A

`e-(1)/(2)e^(2) -(5)/(2)`

B

`e-e^(2)-3`

C

`(1)/(2)(e-3)`

D

`e-(1)/(2) e^(2) - (3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Definite intefral Exercise 1 : Single Option Correct Type Questions|1 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

Let f:R->R be a function satisfying f((x y)/2)=(f(x)*f(y))/2,AAx , y in R and f(1)=f'(1)=!=0. Then, f(x)+f(1-x) is (for all non-zero real values of x ) a.) constant b.) can't be discussed c.) x d.) 1/x

If f is a function satisfying f(x+y)= f(x) f(y) for all x,y in N such that f(1)=3 and sum_(x=1)^n f(x)=120 , find the value of n.

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2, then

If f is a function satisfying f(x+y)=f(x)xxf(y) for all x ,y in N such that f(1)=3 and sum_(x=1)^nf(x)=120 , find the value of n .

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in RR is

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. The value of ("lim")(nvecoo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+s...

    Text Solution

    |

  2. Let f(x) =int-1^x e^(t^2) dt and h(x)=f(1+g(x)), where g (x) is define...

    Text Solution

    |

  3. If f be a function satisfying f(x+y)=f(x)+f(y),AAx,yinR. If f(1) = k, ...

    Text Solution

    |

  4. Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4)) and g be the inverse of f. ...

    Text Solution

    |

  5. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

    Text Solution

    |

  6. Let f be a positive function. Let I(1)=int(1-k)^(k)x f[x(1-x)]dx , I(...

    Text Solution

    |

  7. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

    Text Solution

    |

  8. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx where a is positive r...

    Text Solution

    |

  9. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

    Text Solution

    |

  10. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

    Text Solution

    |

  11. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

    Text Solution

    |

  12. lim(n rarr infty) sum(k=1)^(n) (k)/(n^(2)+k^(2)),x gt 0 is equal to

    Text Solution

    |

  13. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

    Text Solution

    |

  14. Evaluate the definite integral: int0^1((xdx)/(1+x))

    Text Solution

    |

  15. The value of int (0)^(infty)e^-(a^(2)x) dx is equal to

    Text Solution

    |

  16. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

    Text Solution

    |

  17. If 2f (x) +f (-x)=(1)/(x) sin (x-(1)/(x)), then the value of int(1//e...

    Text Solution

    |

  18. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

    Text Solution

    |

  19. If f(x) is differentiable function and (f(x).g(x)) is differentiable a...

    Text Solution

    |

  20. The number of integral solutions of the equation 4int (0)^( infty)(log...

    Text Solution

    |