Home
Class 12
MATHS
A real valued function f(x) satisfies th...

A real valued function f(x) satisfies the functional equation `f(x-y) = f(x) f(y) - f(a-x) f(a+y)`, where a is a given constant and f(0)=1 , f(2a-x) =?

A

`-f(x)`

B

f(x)

C

f(a-x)

D

f(-x)

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - C) Objective Type Questions (More than one option are correct)|17 Videos
  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - D) Linked Comprehension Type Questions|17 Videos
  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - A) Objective Type Questions (one option is correct)|102 Videos
  • PROBABILITY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|11 Videos
  • SEQUENCES AND SERIES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - J) Aakash Challengers|11 Videos

Similar Questions

Explore conceptually related problems

A real-valued functin f(x) satisfies the functional equation f(x-y)=f(x)f(y)-f(a-x)f(a+y), where a given constant and f(0)=1. Then prove that f(x) is symmetrical about point (a, 0).

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (f'(x))^2 = 0

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

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

A function f (x) is defined for all x in R and satisfies, f(x + y) = f (x) + 2y^2 + kxy AA x, y in R , where k is a given constant. If f(1) = 2 and f(2) = 8 , find f(x) and show that f (x+y).f(1/(x+y))=k,x+y != 0 .

Let f(x) be a real valued function satisfying the relation f(x/y) = f(x) - f(y) and lim_(x rarr 0) f(1+x)/x = 3. The area bounded by the curve y = f(x), y-axis and the line y = 3 is equal to

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

AAKASH INSTITUTE ENGLISH-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. Range ofthe function f(x)=cos(Ksin x) is [-1,1], then the least positi...

    Text Solution

    |

  2. Consider that the graph of y = f(x) is symmetrie about the lines x =...

    Text Solution

    |

  3. The domain of f(x) is (0,1) .Then the domain of (f(e^x)+f(1n|x|) is (a...

    Text Solution

    |

  4. If f(x) = 4^(x) - 2^(x + 1) + 5, then range of f(x) is

    Text Solution

    |

  5. Let g be a real valued function defined on the interval (-1, 1) such t...

    Text Solution

    |

  6. If f(x) is a real-valued function defined as f(x)=In (1-sinx), then t...

    Text Solution

    |

  7. if f(x) is a real valued function defined as f(x)={min{|x|,1/x^2,1/x^3...

    Text Solution

    |

  8. Select the correct option

    Text Solution

    |

  9. Let f(x) = [x]^(2) + [x+1] - 3, where [.] denotes the greatest integer...

    Text Solution

    |

  10. If 2^(f(x)) = (2+x)/(2-x), x in (-2, 2) and f(x) = lambda f((8x)/(4+ x...

    Text Solution

    |

  11. If tan ax + cot ax and |tan x| + |cot x| are periodic functions of th...

    Text Solution

    |

  12. If {x} and [x] represent fractional and integral part of x, then [x]+...

    Text Solution

    |

  13. Let g(x) = x - [x] - 1 and f(x) = {{:(-1", " x lt 0),(0", "x =0),(1",...

    Text Solution

    |

  14. If the function f(x) = [4.8 + asinx] (where [.]- * denotes the greates...

    Text Solution

    |

  15. [(4)/(5)] + [(4)/(5)+(1)/(1000)] + [(4)/(5)+(2)/(1000)] + ...+[(4)/(5)...

    Text Solution

    |

  16. A real valued function f(x) satisfies the functional equation f(x-y) ...

    Text Solution

    |

  17. lf f: R rarr R satisfies, f(x + y) = f(x) + f(y), AA x, y in R and f(1...

    Text Solution

    |

  18. Let f: RvecRa n dg: RvecR be two one-one and onto function such that t...

    Text Solution

    |

  19. If f(x+10) + f(x+4)= 0, there f(x) is a periodic function with period

    Text Solution

    |

  20. If f(x) = a(x^n +3), f(1) = 12, f(3) = 36, then f(2) is equal to

    Text Solution

    |