Home
Class 12
MATHS
Let f (x) be a real vaued continuous fun...

Let `f (x)` be a real vaued continuous function such that
`f (0) =1/2 and f(x+y) = f(x) f (4-y) + f(y) f (4-x ) AA x, y in R,` then for some real a:
a. f(x) is a periodic function
b. f(x) is a constant function
c. `f(x)=1/2`
d. `f(x)=(cosx)/2`

A

f(x) is a periodic function

B

f(x) is a constant function

C

`f(x)=1/2`

D

`f(x)=(cosx)/2`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|25 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|76 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 continuous function such that f(0) = 1 and f(x)-f (x/7) = x/7 AA x in R , then f(42) is

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

If 'f' is a real valued differentiable function such that f(x) f'(x) < 0 for all real x, then

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

If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , then

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . The equation f(x)-x-f(0)=0 have exactly

If f(x) is a polynomial function f:R→R such that f(2x)=f (x) f ′′(x) Then f(x) is

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

If f is a real valued differentiable function satisfying | f (x) - f (y) | le (x - y) ^(2) for all real x and y and f (0) =0 then f (1) equals :

ARIHANT MATHS-FUNCTIONS-Exercise (More Than One Correct Option Type Questions)
  1. f(x)=x^2-2a x+a(a+1),f:[a ,oo)⟶[a ,oo)dot If one of the solution of th...

    Text Solution

    |

  2. The function 'g' defined by g(x)=sin(sin^(-1){sqrt(x)}+cos (sin^(-1){s...

    Text Solution

    |

  3. The graph of f:R rarr R defined by y=f(x) is symmetric with respect to...

    Text Solution

    |

  4. Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and ...

    Text Solution

    |

  5. Let f(x)=abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4), then a. least value of ...

    Text Solution

    |

  6. Let A={1,2,3,4,5}, B={1,2,3,4} and f:A rarr B is a function, then

    Text Solution

    |

  7. In a function 2f(x)+ xf(1/x)-2f(|sqrt2sin(pi(x+1/4))|)=4cos^2[(pix)/2]...

    Text Solution

    |

  8. If f(x) is a differntiable function satisfying the condition f(100x)=x...

    Text Solution

    |

  9. If [x] denotes the greatest integer function then the extreme values o...

    Text Solution

    |

  10. Which of the following are true?

    Text Solution

    |

  11. If f(x) is a polynomial of degree n such that f(0)=0 , f(x)=1/2,......

    Text Solution

    |

  12. Let f: R->R be a function defined by f(x+1)=(f(x)-5)/(f(x)-3)AAx in R...

    Text Solution

    |

  13. Let f(x)=1-x-x^3.Find all real values of x satisfying the inequality,...

    Text Solution

    |

  14. If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y i...

    Text Solution

    |

  15. If the fundamental period of function f(x)=sinx+cos(sqrt(4-a^(2)))x "...

    Text Solution

    |

  16. Let f (x) be a real vaued continuous function such that f (0) =1/2 a...

    Text Solution

    |

  17. if f(g(x)) is one-one function, then

    Text Solution

    |

  18. Which of the following functions have their range equal to R(the set o...

    Text Solution

    |

  19. Which of the following pairs of function are identical? a. f(x)=e^(In ...

    Text Solution

    |

  20. Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fra...

    Text Solution

    |