Home
Class 11
MATHS
If f(x)=cos(logx), then show that f((1)/...

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

Text Solution

Verified by Experts

The correct Answer is:
`=0`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-1 (B)|25 Videos

  • FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-1 (C)|34 Videos

  • FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-1 (C)|34 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISE -6(B)|21 Videos

  • HYPERBOLIC FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 9(a)|10 Videos

Similar Questions

Explore conceptually related problems

If f(x) = cos(log x) , 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)=

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

If y=f(x) =(x+2)/(x-1)(x ne 1,-2) then show that x=f(y)

If f(x) = 1 + x + x^(2) + …… for |x| lt 1 then show that f^(-1)(x) = (x-1)/(x) .

If y=f(x)=(2x-1)/(x-2), then f(y)=

If f(x) is a function such that f(xy) = f(x)+f(y) and f(x)=

The function y=f(x) such that f(x+1/x) = x^(2)+(1)/(x^(2))

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-FUNCTIONS -TEXTUAL EXERCISES (EXERCISE-1 (A)
  1. If the function f is defined by f(x) = {{:(x+2, x gt 1),(2, -1 le x...

    Text Solution

    |

  2. If f: R - {0} to R is defined by f(x) = x^(3)-1/(x^3), then S.T f(x) +...

    Text Solution

    |

  3. If f: R to R is defined by f(x)=(1-x^(2))/(1+x^(2)) then show that f(t...

    Text Solution

    |

  4. If f:R-(pm1)toR is defined by f(x)=log|(1+x)/(1-x)|, then show that f(...

    Text Solution

    |

  5. If A={-2,-1,0,1,2} and f:A to B is a surjection defined by f(x)=x^(2)+...

    Text Solution

    |

  6. If A = {1, 2, 3, 4} and f: A to R is a function defined by f(x) = (x^(...

    Text Solution

    |

  7. If f(x+y)=f(xy)AAx,y in R then prove that f is a constane function.

    Text Solution

    |

  8. If A={x:-1 le x le 1},f(x)=x^(2) and g(x)=x^(3), which of the followin...

    Text Solution

    |

  9. If A = { x : -1 le x le 1}, g(x) = x^(3) , which of the following are...

    Text Solution

    |

  10. Which of the following are one-one ,onto (or) bijections? Justify your...

    Text Solution

    |

  11. f : R to (0, oo) defined by f (x) = 2 ^(x) . then f ^-1(x)

    Text Solution

    |

  12. Determine whether the function f:(o,oo) to R defined by f(x) log(e)x i...

    Text Solution

    |

  13. Determine whether the function f:R to [0,oo) defined by f(x)=x^(2) is ...

    Text Solution

    |

  14. If f:[0,infty) to R defined by f(x) = x^(2), then f is

    Text Solution

    |

  15. f: R to R defined by f (x) = x ^(2). then f^-1(x)

    Text Solution

    |

  16. Is g={(1,1),(2,3),(3,5),(4,7)} is a function from A={1,2,3,4}. to B={1...

    Text Solution

    |

  17. If the function f: R to R defined by f(x)=(3^(x)+3^(-x))/(2), then S....

    Text Solution

    |

  18. If the function f: R to R defined by f(x)=(4^(x))/(4^(x)+2), then show...

    Text Solution

    |

  19. If the function f: { -1, 1} to {0,2}, defined by f(x) = ax+b is a surj...

    Text Solution

    |

  20. If f(x)=cos(logx), then show that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/...

    Text Solution

    |