Home
Class 11
MATHS
If f(x+y)=f(x)f(y)AA x,y in R, f(0) ne 0...

`If f(x+y)=f(x)f(y)AA x,y in R, f(0) ne 0` then `F(x) = {f(x)/(1+(f(x)))^2` is

A

even

B

odd

C

both even or odd

D

neither even nor odd

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|81 Videos

  • FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

Let f(x+y)=f(x)f(y)AA x, in IR, f(6)=5 and f'(0)=1 . Then the value of f' (6) is

If f(x+y)+f(x-y)=2f(x).f(y) AA x,y in R . f(0)ne0 , find if f(x) is even or odd function.

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

If f(x + y) = f(x) - f(y), forall x, y in R , then show that f(3) = f(1)

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Let f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0 and f(0)=0 then the value of f(1) +f(2)=

A function f: R -> R satisfies the equation f(x)f(y)-f(x y)=x+yAAx ,y in Ra n df(1)>0 , then a. f(x)f^(-1)(x)=x^2-4 b. f(x)f^(-1)(x)=x^2-6 c. f(x)f^(-1)(x)=x^2-1 d. none of these

If f(x+f(y))=f(x)+yAAx ,y in R a n df(0)=1, then find the value of f(7)dot

If f(x) satisfies the relation f(x + y) = f(x) + f(y) AA x,y in R and f(1) = 5, Find underset (x = 1) overset m sum f(x) Also prove that f(x) is an odd function.

If f : R to R satisfies f(x + y)=f(x)+f(y) for all x, y in R and f(1)=7 , then sum_(r=1)^n f(r)

PATHFINDER-FUNCTION-QUESTION BANK
  1. If - pi/2 lt x lt pi/2, then the range of the function f(x)=cos [x] i...

    Text Solution

    |

  2. If f : R rarr R is defined by f(x)=1/(2-cos3x) for each x in R, then t...

    Text Solution

    |

  3. If f(x+y)=f(x)f(y)AA x,y in R, f(0) ne 0 then F(x) = {f(x)/(1+(f(x)))^...

    Text Solution

    |

  4. A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R ...

    Text Solution

    |

  5. If the function f(x)=[3.5 + b sin x] (where[.] denotes the greatest in...

    Text Solution

    |

  6. Function f(x)=log(x^3+sqrt1+x^6) is

    Text Solution

    |

  7. If the function f satisfies the relation f(x+y)+f(x-y)=2f(x)xxf(y), AA...

    Text Solution

    |

  8. If overset(n) underset (k=0) sum f(x+ka)=0 where a gt 0, then the peri...

    Text Solution

    |

  9. Function f satisfies the equation f(x+a)={(1+f(x))/(1-f(x))} AA x in R...

    Text Solution

    |

  10. If f'(x)={(1-2sin^2x)/(f(x))}, f(x) ge 0, AA x in R and f(0)=1, then ...

    Text Solution

    |

  11. If a, b be two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2 ...

    Text Solution

    |

  12. Period of f(x)=sin, pi/2 x+2cos, pi/3 x-tan, pi/4 x is equal to

    Text Solution

    |

  13. Polynomial function f(x) satisfying the condition f(x), f(1/x)=f(x)+f...

    Text Solution

    |

  14. The function f(x) is defined for all real x. If f(a+b)=f(ab) AA a and...

    Text Solution

    |

  15. If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and ...

    Text Solution

    |

  16. If fog=|sinx| and gof=sin^2 sqrtx then f(x) and f(x) are

    Text Solution

    |

  17. If f is a function such that f(0)=2, f(1)=3 and f(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  18. Let f(x)={(-1+sinK1pix, x is rational), (1+cosK2pix, x is irrational...

    Text Solution

    |

  19. Let f(1)=1 and f(n)=2overset(n-1)underset(r=1)sum f( r ). Then overset...

    Text Solution

    |

  20. Given f(x) = In {(1+x)/(1-x)} and g(x)={(3x+x^3)/(1+3x^2)}. Then f(g(x...

    Text Solution

    |