Home
Class 12
MATHS
If f(x) and g(x) are periodic functions ...

If `f(x) and g(x)` are periodic functions with periods 7 and 11, respectively, then the period of `f(x)=f(x)g(x/5)-g(x)f(x/3)` is

A

177

B

222

C

433

D

1155

Text Solution

Verified by Experts

The correct Answer is:
D
The period of `f(x)` is 7. So, the period of `f((x)/(3)) " is " (7)/(1//3)=21.`
The period of g(x) is 11. So, the period of `g((x)/(5)) " is " (11)/(1//5) =55.`
Hence, `T_(1)="Period of " f(x)g((x)/(5))=7xx 55=385`
and `T_(2)="period of " g(x) f((x)/(3)) =11xx 21 =231`
` :. " Period of " F(x)=LCM {T_(1),T_(2)}`
`=LCM{385,231}`
`=7xx11xx3xx5`
`=1155`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

If f(x) and g(x) are non- periodic functions, then h(x)=f(g(x))is

If f(x+10) + f(x+4), there f(x) is a periodic function with period

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

If f(x) is of period of 7 and g(x) is of period of 11. Then find the period of F(x)=abs({:(f(x),f(x//5)),(g(x),g(x//13)):})

If f(x) and g(x) are periodic functions with the same fundamental period where f(x)=sin alpha x+cos alpha x and g(x)=|sin x|+|cos x|, then alpha is equal to (1)0(2)2(3)4(4)8

The function f(x)=x-[x] is a periodic with period.

If f(x) and g(x) are differentiable function then show that f(x)+-g(x) are also differentiable such that d(f(x)+-g(x))/(dx)=d(f(x))/(dx)+-d(g(x))/(dx)

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

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

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. The period of function 2^({x}) +sin pi x+3^({x//2})+cos pi x (where {...

    Text Solution

    |

  2. The period of the function f(x)= [6x+7]+cospix-6x , where [dot] denote...

    Text Solution

    |

  3. If f(x) and g(x) are periodic functions with periods 7 and 11, respect...

    Text Solution

    |

  4. The period of the function f(x)=c^((sin^2x) +sin^2 (x+pi/3)+cosxcos(x+...

    Text Solution

    |

  5. Let f(x)={(0.1)^(3[x])}. (where [.] denotes greatest integer function ...

    Text Solution

    |

  6. If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= ...

    Text Solution

    |

  7. The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in ...

    Text Solution

    |

  8. If f(x)=(-1)^([2/pi]),g(x)=|sinx|-|cosx|,a n dvarphi(x)=f(x)g(x) (wher...

    Text Solution

    |

  9. If f(x)=1/x ,g(x)=1/(x^2), and h(x)=x^2,t h e n f(x)=x^2,x!=0,(h(g(x...

    Text Solution

    |

  10. If f(x)={(x^(2)",","for "x ge0),(x",","for "x lt 0):}, then fof(x) is...

    Text Solution

    |

  11. Let f(x)=sinx and g(x)=(log)e|x|dot If the ranges of the composition f...

    Text Solution

    |

  12. If f(x)={x ,xi sr a t ion a l1-x ,xi si r r a t ion a l ,t h e nf(f(x)...

    Text Solution

    |

  13. If f and g are one-one functions, then

    Text Solution

    |

  14. The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is

    Text Solution

    |

  15. Let h(x)=|k x+5|,the domain of f(x) be [-5,7], the domain of f(h(xx)) ...

    Text Solution

    |

  16. If f(x)=sinx+cosx and g(x)=x^2-1, then g(f (x)) is invertible in the ...

    Text Solution

    |

  17. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

    Text Solution

    |

  18. Let f(x)=(x+1)^2-1, xgeq-1. Then the set {x :f(x)=f^(-1)(x)} is {0,1,(...

    Text Solution

    |

  19. if f:[1,oo)->[2,oo) is given by f(x)=x+1/x then f^-1(x) equals to

    Text Solution

    |

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

    Text Solution

    |