Home
Class 12
MATHS
Let f(x) be a periodic function with pe...

Let `f(x)` be a periodic function with period `int_0^x f(t+n) dt 3 and f(-2/3)=7 and g(x) =` .where `n=3k, k in N`. Then `g'(7/3) =`

A

`-2/3`

B

7

C

-7

D

`7/3`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|6 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(x) be a periodic function with period int_(0)^(x)f(t+n)dt3 and f(-(2)/(3))=7 and g(x)= where n=3k,k in N. Then g'((7)/(3))=

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nt+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=int_(0)^(x) f(t)dt , then

If y=f(x) is a periodic function with period K, then g(x)=f(ax+b) is a Periodic function,The period of g(x) is

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(2) in terms of k is equal to (A) k (B) 2k (C) 3k (D) 5k

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(x+2)-g(x) is equal to (A) g(1) (B) 0 (C) g(2) (D) g(3)

f is an odd function,It is also known that f(x) is continuous for all values of x and is periodic with period 2. If g(x)=int_(0)^(x)f(t)dt, then g(x) is odd (b) g(n)=0,n in Ng(2n)=0,n in N( d) g(x) is non-periodic

Let f(x) is periodic function such that int _(0) ^(x) (f (t))^(3) dt = (1)/(x ^(2))(int _(0) ^(x) (f(t)dt ) ) ^(3) AA x in R- {0} Find the function f (x) if (1) =1.

If f is periodic,g is polynomial function and f(g(x)) is periodic and g(2)=3,g(4)=7 then g(6) is

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f(x) be a periodic function with period int0^x f(t+n) dt 3 and f...

    Text Solution

    |

  2. If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x), then the value...

    Text Solution

    |

  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

    Text Solution

    |

  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  5. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  6. The function f:[0,3] to [1,29], defined by f(x)=2x^(3)-15x^(2)+36x+1 i...

    Text Solution

    |

  7. Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x sat...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g{f(x)} is invertible in the dom...

    Text Solution

    |

  13. Domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) fo...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Let E={1,2,3,4}a n dF-{1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  18. Suppose f(x)=(x+1)^2forxgeq-1. If g(x) is the function whose graph is ...

    Text Solution

    |

  19. If f:[1,infty) rarr [2,infty) is given by f(x)=x+1/x, " then " f^(-1)(...

    Text Solution

    |

  20. Let f(x0=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x...

    Text Solution

    |

  21. The domain of definition of function of f(x)=(log(2)(x+3))/(x^(2)+3x+2...

    Text Solution

    |