Home
Class 11
MATHS
If f(x)=cos((log)e x),\ t h e n\ f(1/x)f...

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)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA ENGLISH|Exercise All Questions|100 Videos

  • GEOMETRIC PROGRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|256 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)_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(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)=cos^(-1){(1-(log_(e)x)^(2))/(1+(log_(e)x)^(2))}, then f'((1)/( e )) is equal to

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)=|(log)_e x| , then (a) f'(1^+)=1 (b) f^'(1^(-))=-1 (c) f'(1)=1 (d) f'(1)=-1

If f^(prime)(1)=2 and y=f((log)_e x) , find (dy)/(dx) at x=e .

RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. Which of the following are function: {(x , y): y^2=x , x , y in R} b...

    Text Solution

    |

  2. If A={1,2,3},\ B={x , y} , then the number of functions that can be de...

    Text Solution

    |

  3. If x!=1\ a n d\ f(x)=(x+1)/(x-1) is a real function, then f(f(f(2))) ...

    Text Solution

    |

  4. 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 eq...

    Text Solution

    |

  5. Let A={x in R : x!=0,\ -4lt=xlt=4} and f: A->R be defined by f(x)=(|x...

    Text Solution

    |

  6. Let f(x)=x,g(x)=1/x and h(x)=f(x)g(x) . Then h(x)=1 for a.x in R b. x...

    Text Solution

    |

  7. If f: R->R : x!=0,\ -4lt=xlt=4 and f: A->A be defined by f(x)=(|x|)/x ...

    Text Solution

    |

  8. If f: RvecR and g: RvecR are defined by f(x)=2x+3a n dg(x)=x^2+7, then...

    Text Solution

    |

  9. If f: [-2, 2] -> R is defined by f(x)={-1,for -2<=x<=0 , then x...

    Text Solution

    |

  10. If f(x)=64x^3+1/x^3 and alpha,beta are the roots of 4x+1/x=3. Then,val...

    Text Solution

    |

  11. The domain of the function f(x)=sqrt(2-2x-x^2) is [-sqrt(3),\ sqrt(3)]...

    Text Solution

    |

  12. The domain of the function f(x)=((x+1)(x-3))/(x-2) is a. [-1,2)uu[3,o...

    Text Solution

    |

  13. The domain of the function f(x)=sqrt(((x+1)(x-3))/(x-2)) is [-1,2)uu[3...

    Text Solution

    |

  14. The domain of definition of the function f(x)=sqrt(x-1)+sqrt(3-x) is a...

    Text Solution

    |

  15. The domain of definition of the function f(x)=sqrt((x-2)/(x+2))+sqrt((...

    Text Solution

    |

  16. The domain of definition of the function f(x)="log"|x| is a.R b. (-o...

    Text Solution

    |

  17. The domain of definition of f(x)=x-3-2sqrt(x-4)-x-3+2sqrt(x-4) is a. ...

    Text Solution

    |

  18. The domain of the function f(x)=sqrt(5|x|-x^2-6) is (a) (-3,\ -2)uu(...

    Text Solution

    |

  19. The range of the function f(x)=(x+2)/(|x+2|),\ x!=-2 is {-1,1} b. {-1,...

    Text Solution

    |

  20. The range of the function f(x)=x/(|x|) is a.R-{0} b. R-{-1,1} c. {-1,1...

    Text Solution

    |