Home
Class 11
MATHS
If f(x) = cos(log x) then f(x)f(y)-1/2[f...

If `f(x) = cos(log x)` then `f(x)f(y)-1/2[f(x/y)+f(xy)]` has the value

A

0

B

`(1)/(2)f(x) f(y)`

C

`f(x+y)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `f(x)=cos (log _(e) x)`
`therefore f(x) f(y)-(1)/(2){f((x)/(y))+f(xy)}"`
`=cos (log x) cos (log y)-(1)/(2){cos log((x)/(y))+cos (log (x y))}`
`=cos (log x) cos (log y)-(1)/(2){cos (log-x log-y)+cos (log x+log y)}`
`=cos (log x) cos (log y)-(1)/(2){2cos (log x) cos(log y)}`
=0
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|49 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

If f(x)=cos((log)_e x),\ t h e n\ f(1/x)f(1/y)-1/2{f(x y)+f(x/y)} is equal to a. "cos"(x-y) b. log(cos(x-y)) c. 0 d. "cos"(x+y)

If f(x)=cos(logx) , then f(x^(2))f(y^(2))-(1)/(2)[f(x^(2)y^(2))+f((x^(2))/(y^(2)))]=

If f(x)=sin(logx) then f(xy)+f(x/y)-2f(x)cos(logy)= (A) cos(logx) (B) sin(logy) (C) cos(log(xy)) (D) 0

If f(x+y,x -y)= xy then (f(x,y)+f(y,x))/(2)=

If f(x)=cos(logx) , then prove that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/(y))+f(xy)]=0

If f(x)=log_(e)x, then prove that :f(xyz)=f(x)+f(y)+f(z)

If f'(x)=sin(log x)and y=f((2x+3)/(3-2x)), then dy/dx equals

Let f(x) is a polynomial satisfying f(x).f(y) = f(x) +f(y) + f(xy) - 2 for all x, y and f(2) = 1025, then the value of lim_(x->2) f'(x) is

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Chapter Test
  1. If f(x) = cos(log x) then f(x)f(y)-1/2[f(x/y)+f(xy)] has the value

    Text Solution

    |

  2. The number of bijective functions from set A to itself when A contains...

    Text Solution

    |

  3. If f(x)=|sin x| then domain of f for the existence of inverse of

    Text Solution

    |

  4. The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=s in^(...

    Text Solution

    |

  5. Let f: R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x)...

    Text Solution

    |

  6. If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is - (a)f is one-...

    Text Solution

    |

  7. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) , where m!=n...

    Text Solution

    |

  8. Find the inverse of the function: f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x))+2

    Text Solution

    |

  9. Find the inverse of the function :y=(1 0^x-1 0^(-x))/(1 0^x+1 0^(-x))+...

    Text Solution

    |

  10. Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals

    Text Solution

    |

  11. Let f : R rarr R, g : R rarr R be two functions given by f(x) = 2x - 3...

    Text Solution

    |

  12. If g(x)=1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) is equal to

    Text Solution

    |

  13. If f(x)=(1-x)/(1+x), x ne 0, -1 and alpha=f(f(x))+f(f((1)/(x))), then

    Text Solution

    |

  14. Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...

    Text Solution

    |

  15. If f:(-oo,2]to (-oo,4] where f(x), then f ^(-1) (x) is given by :

    Text Solution

    |

  16. Find the inverse of the function, (assuming onto). " " ...

    Text Solution

    |

  17. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

    Text Solution

    |

  18. If f(x)=log((1+x)/(1-x))a n dt h e nf((2x)/(1+x^2)) is equal to {f(x)...

    Text Solution

    |

  19. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to 1/2{f(2x)+f(2y...

    Text Solution

    |

  20. The function f:R to R given by f(x)=x^(2)+x is

    Text Solution

    |

  21. Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for ...

    Text Solution

    |