Home
Class 11
MATHS
Let f(x)=(alphax)/(x+1),x!=-1. Then writ...

Let `f(x)=(alphax)/(x+1),x!=-1.` Then write the value of `alpha` satisfying `f(f(x))=x` for all `x!=-1.`

Text Solution

Verified by Experts

We have,
`f{f(x)}=x ` for all `x !=0`
`=> f((alphax)/(x+1))=x` for all `x!=1`
`=> ((alpha((alphax))/(x+1))/(((alphax)/(x+1))+1)=x` for all `x!=0`
...
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos

  • GEOMETRIC PROGRESSIONS

    RD SHARMA|Exercise Solved Examples And Exercises|255 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=(alpha x)/(x+1), x ne -1. Then, for what value of alpha " is " f[f(x)]=x ?

Let f(x)=(alphax)/(x+1),x ne -1 . Then, for what values of alpha is f[f(x)]=x?

Let f(x)=(alpha x)/(x+1) Then the value of alpha for which f(f(x)=x is

Let f(x)=(alpha x)/((x+1)),x!=-1. The for what value of alpha is f(f(x))=x( a )sqrt(2)(b)-sqrt(2)(c)1

" Let "f(x)=(alpha x)/(x+1),x!=-1" and "f(f(x))=x" ,then the value of "(alpha^(2))/(2)" is "

Let f(x)=(kx)/(x+1) then the value of k such that f(x) is

Let f(x)=x+1 and phi(x)=x-2. Then the value of x satisfying |f(x)+phi(x)|=|f(x)|+|phi(x)| are :

Let f(x) = (alpha x^(2))/(x + 1), x ne - 1 , The value of alpha for which f(a) = a , (a ne 0 ) is

RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. If 2f(x)-3f(1/x)=x^2(x!=0), then f(2) is equal to (a)-7/4("b")""5/...

    Text Solution

    |

  2. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to (a) 1/2{f(2...

    Text Solution

    |

  3. Let f(x)=(alphax)/(x+1),x!=-1. Then write the value of alpha satisfyin...

    Text Solution

    |

  4. Write the range of the function f(x)=sin[x],w h e r e(-pi)/4lt=xlt=pi/...

    Text Solution

    |

  5. If f(x)=log((1+x)/(1-x))a n dg(x)=((3x+x^3)/(1+3x^2)) , then f(g(x)) i...

    Text Solution

    |

  6. If f(x) = cos(log x) then f(x^2)f(y^2)-1/2[f(x^2y^2)+f(x^2/y^2)] has t...

    Text Solution

    |

  7. Relation between graphs of a function and its inverse

    Text Solution

    |

  8. A be the set of two positive integers and f: A -> Z^+ (set of positiv...

    Text Solution

    |

  9. Range of f(x) =1/(1-2cosx) is (1) [1/3,1] (2) [-1,1/3] (3) (-o...

    Text Solution

    |

  10. Let f:[2,oo) rarr R and g:[-2,oo) rarr R be to two real functions defi...

    Text Solution

    |

  11. Find the domain of each of the following real valued functions of real...

    Text Solution

    |

  12. Examples :- If x;yin{1;2;3;4};then which of the following are function...

    Text Solution

    |

  13. Find the domain and range of the function f={(x :1/(1-x^2)): x in R ...

    Text Solution

    |

  14. Express the following functions as sets of ordered pairs and determine...

    Text Solution

    |

  15. if for nonzero x, af(x) + bf(1/x) =1/x-5, where a!=b then f(2) =

    Text Solution

    |

  16. If f(x) = (a-x^n)^(1/n), a > 0 and n in N, then prove that f(f(x)) = x...

    Text Solution

    |

  17. If f(x)=(x-1)/(x+1) , then show that f(1/x)=-f(x) (ii) f(-1/x)=-1/(f(...

    Text Solution

    |

  18. Find the domain and range of the function f(x) given by f(x)=(x-2)/(3-...

    Text Solution

    |

  19. Find range of each of the following functions:

    Text Solution

    |

  20. Is g={(1,1),(2,3),(3,5),(4,7)} a function? If this is described by th...

    Text Solution

    |