Home
Class 12
MATHS
Let f: R^+ ->R be a function which sati...

Let `f: R^+ ->R` be a function which satisfies `f(x)dotf(y)=f(x y)+2(1/x+1/y+1)` for `x , y > 0.` Then find `f(x)dot`

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x ,AAx in Rdot Then find the value of f(0)dot

A continuous function f(x)onR->R satisfies the relation f(x)+f(2x+y)+5x y=f(3x-y)+2x^2+1forAAx ,y in R Then find f(x)dot

A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R then f is

If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then find f(x).

Consider f: R^(+)->R such that f(3)=1 for a in R^+ a n d """"f(x)dotf(y)+ f(3/x)f(3/y)=2f(x y)AAx ,y in R^+dot Then find f(x)dot

If a function satisfies (x-y) f(x+y)-(x+y) f(x-y) = 2(x^2y - y^3), AA x, y in R and f(1) = 2, then

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot

If the function f satisfies the relation f(x+y)+f(x-y)=2f(x)xxf(y), AA x, y, in R and f(0) ne 0 , then

f(x) is real valued function, satisfying f(x+y)+f(x-y)=2f(X),f(y) for all y ne R , then

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Find the domain of the function : f(x)=sin^(-1)((log)2x)

    Text Solution

    |

  2. Each question has four choices, a,b,c and d,out of which only one is ...

    Text Solution

    |

  3. Let f: R^+ ->R be a function which satisfies f(x)dotf(y)=f(x y)+2(1/x...

    Text Solution

    |

  4. Find Domain of the following function : f(x)=log(x-4)(x^2-11x+24)

    Text Solution

    |

  5. If g:[-2,2]rarrR , where f(x)=x^3+tanx+[(x^2+1)/P] is an odd functio...

    Text Solution

    |

  6. A continuous function f(x)onR->R satisfies the relation f(x)+f(2x+y)+5...

    Text Solution

    |

  7. Find the range of the following function f(x)=log2"((sinx-cosx+3sqrt2...

    Text Solution

    |

  8. Prove that f(x)gi v e nb yf(x+y)=f(x)+f(y)AAx in R is an odd function...

    Text Solution

    |

  9. If f(x)=sin([x]pi)/(x^2+x+1)where [.] denotes the greatest integer fu...

    Text Solution

    |

  10. Find the value of x in [-pi,pi] for which f(x)=sqrt((log)2(4sin^2x-2s...

    Text Solution

    |

  11. If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that ...

    Text Solution

    |

  12. Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfie...

    Text Solution

    |

  13. Find the domain of f(x)=sqrt(x-4-2sqrt((x-5)))-sqrt(x-4+2sqrt((x-5)))

    Text Solution

    |

  14. Let f(x) be periodic and k be a positive real number such that f(x+k)+...

    Text Solution

    |

  15. Find the domain of the following functions: f(x)=(x-3)/((x+3)sqrt(x^2-...

    Text Solution

    |

  16. Let S be the set of all triangles and R^+ be the set of positive real ...

    Text Solution

    |

  17. Check whether the function defined by f(x+lambda)=1+sqrt(2f(x)-f^2(x))...

    Text Solution

    |

  18. Solve (x-1)^2(x+4)<0

    Text Solution

    |

  19. If f(x)={x ,x is rational 1-x ,x is irrational ,then f(f(x)) is

    Text Solution

    |

  20. An odd function is symmetric about the vertical line x=a ,(a >0),a n d...

    Text Solution

    |