Home
Class 11
MATHS
If f(x) = cos (log (e) x), then f (x) f(...

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

A

`-1`

B

`1/2`

C

`-2`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|83 Videos

  • PROBABILITY

    TARGET PUBLICATION|Exercise EVALUATION TEST|8 Videos

  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

Similar Questions

Explore conceptually related problems

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

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

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

If f(x)=cos(ln x) then f(x)f(y)-(1)/(2)(f((x)/(y))+f(xy)) has the value

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

TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. If f: R to R be defined by f(x)={(2x:xgt3),(x^(2):1lt x le 3),(3x:x le...

    Text Solution

    |

  2. Let f : R to R satisfy f (x) (2) =4, then f ((1)/(2))=

    Text Solution

    |

  3. If f(x) = cos (log (e) x), then f (x) f(y) -1/2 [f(xy) +f((x)/(y))] ha...

    Text Solution

    |

  4. The values of ba n dc for which the identity of f(x+1)-f(x)=8x+3 is sa...

    Text Solution

    |

  5. Given the function f (x) =(a ^(x) + a ^(-x))/(2), a gt 2, then f (x+y)...

    Text Solution

    |

  6. If f(x) = log ((1+x)/(1-x)), then f((2x)/(1+x^(2))) is equal to

    Text Solution

    |

  7. If e^(f(x))=(10+x)/(10-x), x in (-10, 10) and f(x)=kf ((200x)/(100+x^(...

    Text Solution

    |

  8. If f(x) =cos [pi^(2)]x+ cos [-pi^(2)] x, where [x] denots the greatest...

    Text Solution

    |

  9. Prove that if f (x) is periodic function with period T, then the funct...

    Text Solution

    |

  10. If the graph of the function y = f(x) is symmetrical about the line x ...

    Text Solution

    |

  11. Let f {(1,1), (2,4), (0,-2), (-1,-5)} be a linear function from Z into...

    Text Solution

    |

  12. If f (x) =log ""(1+x)/(1-x) then-

    Text Solution

    |

  13. The real valued function f(x)=(a^x-1)/(x^n(a^x+1)) is even, then the v...

    Text Solution

    |

  14. The function f(x) = sec[log(x + sqrt(1+x^2))] is

    Text Solution

    |

  15. The function f(x)= sin | log (x+ sqrt(x^(2) +1)) | is-

    Text Solution

    |

  16. If f(x)+2f((1)/(x))=3x, x ne 0 and S={x in R: f(x) = f(-x)}, " then ...

    Text Solution

    |

  17. If [x] denotes the greatest integer le x, then [(2)/(3)]+[(2)/(3)+(1)/...

    Text Solution

    |

  18. f(x)=cos^(2)x+cos^(2)(pi/3+x)-cosx*cos(x+pi/3) is

    Text Solution

    |

  19. If y=f(x)=((x+2))/((x-1)),t h e n x=f(y) (b) f(1)=3 y increases wit...

    Text Solution

    |

  20. If g (y) is inverse of function f :R to R given by f (x)=x+3, then g (...

    Text Solution

    |