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`

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • FUNCTIONS

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

  • FUNCTIONS

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

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|72 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

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

If a function f: R ->R be such that f(x-f(y)) = f(f(y) )+xf(y)+f(x) -1 AA x , y in R then f(2)=

Let f(x) be a continuous function, AA x in R, f(0) = 1 and f(x) ne x for any x in R , then show f(f(x)) gt x, AA x in R^(+)

If f be decreasing continuous function satisfying f(x + y) = f(x) + f(y)-f(x) f(y) Y x, y epsilon R ,f'(0)=1 then int_0^1 f(x)dx is

If f(x) is a real valued function such that f(x + 6) - f(x + 3) + f(x) = 0, AA x in R , then period of f(x) is

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is

Let f be a real valued function satisfying 2f(xy) = {f(x)}^(y) + {f(y)}^(x), AA x, y in R and f(1) = 2, then find underset(K = 1)overset(2008)sum f(K)

Let f(x) be a function such that f(x).f(y)=f(x+y) , f(0)=1 , f(1)=4 . If 2g(x)=f(x).(1-g(x))

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

ARIHANT MATHS ENGLISH-FUNCTIONS-Exercise (More Than One Correct Option Type Questions)
  1. If the following functions are defined from [-1,1]to[-1,1], select tho...

    Text Solution

    |

  2. Let f(x)={{:(x^(2)-4x+3",", x lt 3),(x-4",", x ge 3):} and g(x)={{:(...

    Text Solution

    |

  3. f(x)=x^2-2a x+a(a+1),f:[a ,oo)vec[a ,oo)dot If one of the solution of ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Let f be the continuous and differentiable function such that f(x)=f(2...

    Text Solution

    |

  7. Let f(x)=abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4), then

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    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?

    Text Solution

    |

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

    Text Solution

    |