Home
Class 12
MATHS
f(x) is a real valued function, satisfyi...

f(x) is a real valued function, satisfying f(x+y)+f(x-y)=2f(x).f(y) for all `yinR`, Then

A

f(x) is an even function

B

f(x) is even if f(0)=1

C

f(x) is odd if f(0)=0

D

f(x) is even if f(0)=0

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    FIITJEE|Exercise EXERCISES|43 Videos

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-I|24 Videos

  • FUNCTION

    FIITJEE|Exercise SOLVED PROBLEMS (SUBJECTIVE)|17 Videos

  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

Similar Questions

Explore conceptually related problems

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1_ =a. Then , f (x) =

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=

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

If f is a real valued function not identically zero,satisfying f(x+y)+f(x-y)=2f(x)*f(y) then f(x)

A real valued function f(x) is satisfying f(x+y)=yf(x)+xf(y)+xy-2 for all x,y in R and f(1)=3, then f(11) is

Let be a real function satisfying f(x)+f(y)=f((x+y)/(1-xy)) for all x ,y in R and xy ne1 . Then f(x) is

FIITJEE-FUNCTION-SOLVED PROBLEMS (OBJECTIVE)
  1. For abs(x-1)+abs(x-2)+abs(x-3)le6, x belongs to

    Text Solution

    |

  2. The range of the function y =sqrt( -2cos^2 x + 3 cosx-1) is

    Text Solution

    |

  3. Given f(x)=log(10)((1+x)/(1-x)) and g(x)=(3x+x^(3))/(1+3x^(2)), then f...

    Text Solution

    |

  4. f(x)=(cosx)/([(2x)/pi]+1/2), where x is not an integral multiple of pi...

    Text Solution

    |

  5. The domain of the function f(x)=1/(^((10)C()(x-1)-3x(10)C()x)) contain...

    Text Solution

    |

  6. If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

    Text Solution

    |

  7. If f(x)=([{x}]tan^(-1)((x^(2)-3x-1)/(x^(2)-3x-5))+3-x^(7))^(1/7). Wher...

    Text Solution

    |

  8. If domain of y=f(x) is xin[-3,2], then the domain of f([x]) is

    Text Solution

    |

  9. If the functions f(x) and g(x) are defined on R -> R such that f(x)=...

    Text Solution

    |

  10. If f^(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 an...

    Text Solution

    |

  11. If S is the set of all real numbers x for which > 0 (2x-1)/(2x^3+3x^2+...

    Text Solution

    |

  12. If f'(x)=(1-2sin^(2)x)/(f(x)),(f(x)ge0,AAxinR "and" f(0)=1) then f(x) ...

    Text Solution

    |

  13. f(x) is a real valued function, satisfying f(x+y)+f(x-y)=2f(x).f(y) fo...

    Text Solution

    |

  14. If y is a function of x given by 2log (y-1)-log x-log (y-2)=0, then

    Text Solution

    |

  15. If alpha and beta are two consecutive roots of f(x) = 0, then

    Text Solution

    |

  16. Let f: X to Y be a function defined by f(x) = 2sin(abs(x)+(pi)/4)- sqr...

    Text Solution

    |

  17. Let X be the set of all positive integers greater than or equal to 8 a...

    Text Solution

    |

  18. Number of elements in the range of f(x) = [abs(sinx) + abs(cosx)] is

    Text Solution

    |

  19. Number of solutions of the equation log("sinx + cosx") sqrt2 - (-1 + 2...

    Text Solution

    |

  20. f(x) is a polynomial function satisfying f(x) . f(y) = f(x) + f(y) + f...

    Text Solution

    |