Home
Class 11
MATHS
If overset(n) underset (k=0) sum f(x+ka)...

If `overset(n) underset (k=0) sum f(x+ka)=0` where `a gt 0`, then the period of f(x) is

A

a

B

`(n+1)a`

C

`a/n+1`

D

f(x) is non-periodic

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|81 Videos
  • FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

Let f(1)=1 and f(n)=2overset(n-1)underset(r=1)sum f( r ) . Then overset(m) underset(n=1)sum f(n) is equal to

Let f(x) = x^(3) e^(-3x) , x gt 0 . Then the maximum value of f(x) is:

f(x) ={{:(0, x=0),(x-3, x gt 0):} The function f(x) is:

If f(2a-x)=-f(x), then overset(2a)underset(0)intf(x)dx =

Let f'(x)gt0 and g'(x)lt0 for all x in R, then

Let f(x)={((sin pix)/(5x),"when "x ne 0),(k,"when "x=0):} If f(x) is continuous at x=0, then the value of k is -

Let f(x) be periodic and k be a positive real number such that f(x+k)+f(x)=0fora l lx in Rdot Prove that f(x) is periodic with period 2kdot

If y=f{f(x)} , f(0) =0 and f'(0)=5, then the value of [(dy)/(dx)]_(x=0) is-

If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a gt b gt 0) are constants, then prove that f(x) is a periodic function.

If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a gt b gt 0) are constants, then prove that f(x) is a periodic function.

PATHFINDER-FUNCTION-QUESTION BANK
  1. Function f(x)=log(x^3+sqrt1+x^6) is

    Text Solution

    |

  2. If the function f satisfies the relation f(x+y)+f(x-y)=2f(x)xxf(y), AA...

    Text Solution

    |

  3. If overset(n) underset (k=0) sum f(x+ka)=0 where a gt 0, then the peri...

    Text Solution

    |

  4. Function f satisfies the equation f(x+a)={(1+f(x))/(1-f(x))} AA x in R...

    Text Solution

    |

  5. If f'(x)={(1-2sin^2x)/(f(x))}, f(x) ge 0, AA x in R and f(0)=1, then ...

    Text Solution

    |

  6. If a, b be two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2 ...

    Text Solution

    |

  7. Period of f(x)=sin, pi/2 x+2cos, pi/3 x-tan, pi/4 x is equal to

    Text Solution

    |

  8. Polynomial function f(x) satisfying the condition f(x), f(1/x)=f(x)+f...

    Text Solution

    |

  9. The function f(x) is defined for all real x. If f(a+b)=f(ab) AA a and...

    Text Solution

    |

  10. If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and ...

    Text Solution

    |

  11. If fog=|sinx| and gof=sin^2 sqrtx then f(x) and f(x) are

    Text Solution

    |

  12. If f is a function such that f(0)=2, f(1)=3 and f(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  13. Let f(x)={(-1+sinK1pix, x is rational), (1+cosK2pix, x is irrational...

    Text Solution

    |

  14. Let f(1)=1 and f(n)=2overset(n-1)underset(r=1)sum f( r ). Then overset...

    Text Solution

    |

  15. Given f(x) = In {(1+x)/(1-x)} and g(x)={(3x+x^3)/(1+3x^2)}. Then f(g(x...

    Text Solution

    |

  16. If f: [2,3) rarr [0,1) is defined by f(x)=x-[x], the fractional part o...

    Text Solution

    |

  17. The domain of y=cos^-1((1-2|x|)/3)+log|x-1|x is

    Text Solution

    |

  18. Let f:[-pi/3, 2pi/3] rarr [0,4] be a function defined as f(x)=sqrt3 si...

    Text Solution

    |

  19. Let n be a positive integer with f(n)=1!+2!+3!+….+n! and P(x) and Q(x)...

    Text Solution

    |

  20. A function f:R rarr R is defined by f(x+y)-kxy=f(x)+2y^2, AA xy in R a...

    Text Solution

    |