Home
Class 12
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

-1

B

`1//2`

C

-2

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=cos(logx)`
or `f(x)f(y)-(1)/(2)[f((x)/(y))+f(xy)]`
`=cos(logx)cos(logy)-(1)/(2)[cos(logx-logy)]+[cos(logx+logy)]`
`=cos(logx)cos (logy)-(1)/(2)[2cos(logx)cos(logy)]`
`=0`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.15|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 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

CENGAGE ENGLISH-RELATIONS AND FUNCTIONS-Single Correct Answer Type
  1. Which of the following functions is an injective (one-one) function in...

    Text Solution

    |

  2. Given the function f(x)=(a^x+a^(-x))/2(w h e r ea >2)dotT h e nf(x+y)+...

    Text Solution

    |

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

    Text Solution

    |

  4. The domain of the function f(x)=(1)/(sqrt(""^(10)C(x-1)-3xx""^(10)C(x)...

    Text Solution

    |

  5. The domain of the function f(x)=(sin^(-1)(3-x))/("In"(|x|-2)) is

    Text Solution

    |

  6. The domain of f9x)=((log)2(x+3))/(x^2+3x+2) is R-{-1,2} (b) (-2,oo) ...

    Text Solution

    |

  7. The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the gre...

    Text Solution

    |

  8. The domain of the function f(x)=(log)(3+x)(x^2-1) is (-3,-1)uu(1,oo) ...

    Text Solution

    |

  9. Domain of the function, f(x)=[log10 ((5x-x^2)/4)]^(1/2) is

    Text Solution

    |

  10. The domain of f(x)=log|logx| is

    Text Solution

    |

  11. If x^3f(x)=sqrt(1+cos2x)+|f(x)|, (-3pi)/4ltxlt(-pi) /2 and f(x)=(alpha...

    Text Solution

    |

  12. The function f(x)=(sec^(-1)x)/(sqrt(x-[x]), where [x] denotes the grea...

    Text Solution

    |

  13. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |

  14. The domain of f(x)=cos^(-1)((2-|x|)/4)+[l log(3-x)]^1 is [-2,6] (b...

    Text Solution

    |

  15. The domain of the function f(x)=sqrt(log((1)/(|sinx|)))

    Text Solution

    |

  16. Domain of definition of the function f(x) = log2 (-log(1/2) (1+x^(-4))...

    Text Solution

    |

  17. The number of real solutions of the (log)(0. 5)|x|=2|x| is (a) 1 (b) ...

    Text Solution

    |

  18. Let f: Rvec[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the s...

    Text Solution

    |

  19. The domain of the function f(x)=sqrt(1n((|x|-1))(x^2+4x+4)) is (-3,-1...

    Text Solution

    |

  20. The domain of f(x)=1n(a x^3+(a+b)x^2+(b+c)x+c), where a >0,b^2-4a c=0,...

    Text Solution

    |