Home
Class 11
MATHS
If f is a real function satisfying f(x+1...

If `f` is a real function satisfying `f(x+1/x)=x^2+1/(x^2)` for all `x in R-{0}` , then write the expression for `f(x)` .

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:RrarrR is a function satisfying the property f(x+1)+f(x+3)=2" for all" x in R than f is

If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , then evaluate int_(sintheta)^(cos e ctheta)f(x)dx

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

Let be a real function satisfying f(x)+f(y)=f((x+y)/(1-xy)) for all x ,y in R and xy ne1 . Then f(x) is

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If f(x) is a function satisfying f((1)/(x))+x^(2)f(x)=0 for all non zero x then, int_(sin theta)^("cosec" theta) f(x)dx equals

If a function satisfies the condition f(x+1/x)=x^(2)+1/(x^(2)),xne0 , then domain of f(x) is

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. Find the domain of the real function f(x) defined by f(x)=sqrt((1-|x|)...

    Text Solution

    |

  2. Let f be the exponential function and g be the logarithmic function, F...

    Text Solution

    |

  3. If f is a real function satisfying f(x+1/x)=x^2+1/(x^2) for all x in ...

    Text Solution

    |

  4. Let f\ be a relation on the set NN of natural numbers defined by f={(...

    Text Solution

    |

  5. Let f be the subset of Z xxZ defined by f" "=" "{(a b ," "a" "+" "b)" ...

    Text Solution

    |

  6. Consider a rule f(x)=2x-3 associating elements of NN (set of natural n...

    Text Solution

    |

  7. Let A={-2,\ -1,\ 0,\ 1,\ 2}a n d\ f: A->ZZ be given y f(x)=x^2-2x-3. F...

    Text Solution

    |

  8. Let A={1,2},\ B={3,6} and f: A->B given by f(x)=x^2+2\ and\ g: A->B gi...

    Text Solution

    |

  9. Let f : R - {2} rarr R be defined as f(x) = (x^2 - 4)/(x-2) and g: R...

    Text Solution

    |

  10. Let f: ZZ->ZZ\ a n d\ g: ZZ->ZZ\ be functions defined by f={(n , n^2)...

    Text Solution

    |

  11. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){-5}

    Text Solution

    |

  12. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){26}

    Text Solution

    |

  13. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){10 , 37}

    Text Solution

    |

  14. Let f" "=" "{(1,1)," "(2," "3)," "(0, -1)," "(-1," "-3)} be a function...

    Text Solution

    |

  15. If f: RR->RR be defined as follows: f(x)={1,\ if\ x in QQ, -1,\ if\...

    Text Solution

    |

  16. If f: R->R be defined as follows: f(x)={1,\ if\ x in Q-1,\ if\ x !in ...

    Text Solution

    |

  17. Define a  function as a set of ordered pairs.

    Text Solution

    |

  18. Define a function as a correspondence between two sets.

    Text Solution

    |

  19. Let A={-2,\ -1,\ 0,\ 1,\ 2}a n d\ f: A->Z be given y f(x)=x^2-2x-3. Fi...

    Text Solution

    |

  20. Let A={-2,\ -1,\ 0,\ 1,\ 2}a n d\ f: A->Z be given y f(x)=x^2-2x-3. Fi...

    Text Solution

    |