Home
Class 12
MATHS
Let 'f' be a non-zero real valued contin...

Let 'f' be a non-zero real valued continuous function satisfying f(x + y) = f(x), f(y) . f(y) for all ` x, y in R ` if f(2) = 9 , then f(6) =

A

`3^2`

B

`3^6`

C

`3^4`

D

`3^3`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND CONTINUITY

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise 2(Special Type Questions)|10 Videos
  • LIMITS AND CONTINUITY

    DIPTI PUBLICATION ( AP EAMET)|Exercise SET-3Match The Following|2 Videos
  • LIMITS AND CONTINUITY

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise 1B( One Sided Limits)|71 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) (SET - 4)|5 Videos
  • LINEAR PROGRAMMING [APPENDIX-2]

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise -1|33 Videos

Similar Questions

Explore conceptually related problems

Let f be a non zero continuous function satisfying f(x+y)=f(x) f(y) for all x, y in R . If f(2)=9 then f(3) is

f: R^(+) rarr R is continuous function satisfying f(x/y)=f(x) - f (y) AA x, y in R^(+) . If f'(1) = 1, then

If f is differentiable , f(x+y) = f(x) f(y) for all x, y in R , f(3) =3, f'(0) = 11, then f'(3) =

If f(x) satisfies the relation f(x+ y) = f ( x) + f( y ) for all x, y in R and f(1) = 5 then

The number of linear functions of f satisfying f(x+f(x))=x+f(x) for all x in R is

The number of real linear functions f(x) satisfying f(f(x)) = x + f(x) is

DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. The function f(x)={{:(,3x-1,"if "x lt 1),(,x^(2),"if "x gt 2):}} is co...

    Text Solution

    |

  2. If f: RR to RR is defined by f(x)={{:(,(x+2)/(x^(2)+3x+2),"if "x in R-...

    Text Solution

    |

  3. Let 'f' be a non-zero real valued continuous function satisfying f(x ...

    Text Solution

    |

  4. If f(x+y)=f(x) f(y) and f(x)=1+g(x), h(x)" where "underset(x to 0)"Lt"...

    Text Solution

    |

  5. Let f(x)=f(x) f(y) for all x and y. If f(x) is continuous at x=1. then...

    Text Solution

    |

  6. A discontinuous function y=f(x) satisfying x^(2)+y^(2)=4" is given by ...

    Text Solution

    |

  7. The discontinuous points of f(x)=(1)/(log |x|)" are "

    Text Solution

    |

  8. If f : R to R is defind by f (x) = x - [x], where [x] , is the gr...

    Text Solution

    |

  9. If f : R to R is a continuous defined by f(x)=[x]cos ((2x-1)/(2))pi, w...

    Text Solution

    |

  10. f(x)=sqrt(x-[x]) is discontinuous at

    Text Solution

    |

  11. The value of f(0) so that f(x)=(1+x)^(5//x) is continuous at x=0 is

    Text Solution

    |

  12. The value of f(0) so that f(x)=(sin x)/(x) is continuous at x=0 is

    Text Solution

    |

  13. The value of f(0) so that f(x)=(3x+4 tan x)/(x) is continuous at x=3 i...

    Text Solution

    |

  14. The value of f(0) so that f(x)=(3x+4 tan x)/(x) is continuous at x=0 i...

    Text Solution

    |

  15. The value of f(0) so that f(x)=(sqrt(1+x)-1)/(x) is continuous at x=0 ...

    Text Solution

    |

  16. If f(x)=x^(1/(x-1))" for "x ne 1 and if f is continuous at x=1 then f(...

    Text Solution

    |

  17. The value of f(0) so that the function f(x)=((27-2x)^(1//3)-3)/(9-3(24...

    Text Solution

    |

  18. In order that the function f(x)=(x+1)^(cot x) is continous at x=0, f(0...

    Text Solution

    |

  19. The value of f(00) so that the function f(x)=(2x-Sin^(-1)x)/(2x+Tan^(-...

    Text Solution

    |

  20. The value of f(0) so that the function f(x)=(sqrt(1+x)-root3(1+x))/(x)...

    Text Solution

    |