Home
Class 11
MATHS
If f:[1,oo) to [2, oo)" is given by " f(...

If `f:[1,oo) to [2, oo)" is given by " f(x)=x+(1)/(x), " then " f^(-1)(x)` equals

A

`(x+sqrt(x^(2)-4))/(2)`

B

`(x)/(1+x^(2))`

C

`(x-sqrt(x^(2)-4))/(2)`

D

`1+sqrt(x^(2)-4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, `f:[1,oo] to [2,oo]` is a bijection.
Let f(x)=y. Then,
f(x)=y
`Rightarrow x+(1)/(x)=y`
`Rightarrow x^(2)-xy+1=0`
`Rightarrow x^(2)-xy+1=0`
`Rightarrow x=(y+sqrt(y^(2)-4))/(2)" "[therefore x ge 1]`
`Rightarrow f^(-1)(y)=(y+sqrt(y^(2)-4))/(2)`
`"Hence," f^(-1)(x)=(x+sqrt(x^(2)-4))/(2)"for all "x in[1,oo]`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|48 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equals \ \ (a) (x+sqrt(x^2-4))/2 (b) x/(1+x^2) (c) (x-sqrt(x^2-4))/2 (d) 1+sqrt(x^2-4)

if f:[1,oo)->[2,oo) is given by f(x)=x+1/x then f^-1(x) equals to : a) (x+sqrt(x^2-4))/2 b) x/(1+x^2) c) (x-sqrt(x^2-4))/2 d) 1+sqrt(x^2-4)

If f:[1, oo) rarr [1, oo) is defined as f(x) = 3^(x(x-2)) then f^(-1)(x) is equal to

Let f:[4,oo)to[4,oo) be defined by f(x)=5^(x^((x-4))) .Then f^(-1)(x) is

If f : [0, oo) rarr [0, oo) and f(x) = (x^(2))/(1+x^(4)) , then f is

A function f:(0,oo) -> [0,oo] is given by f(x)=|1-1/x| , then f(x) is (A) Injective but not surjective (B) Injective and bijective (C) Injective only (D) Surjective only

Let f" [1,2] to (-oo,oo) be given by f(x)=(x^(4)+3x^(2)+1)/(x^(2)+1) then find value of in [f_(max)]" in "[-1,2] where [.] is greatest integer function :

Let f:(-oo,2] to (-oo,4] be a function defined by f(x)=4x-x^(2) . Then, f^(-1)(x) is

If f:[0,oo) to [0,1), " and " f(x)=(x)/(1+x) then check the nature of the function.

If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Section I - Solved Mcqs
  1. Let A={x inR: x >=1/2} and B={x in R: x>=3/4}. If f:A->B is defined as...

    Text Solution

    |

  2. Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=...

    Text Solution

    |

  3. If f:[1,oo) to [2, oo)" is given by " f(x)=x+(1)/(x), " then " f^(-1)(...

    Text Solution

    |

  4. Let g(x)=1+x-[x] and f(x)={-1,x < 0 0, x=0 1, x > 0. Then for all...

    Text Solution

    |

  5. Let f(x)=(alphax)/((x+1)),x!=-1. for what value of alpha is f(f(x))=x ...

    Text Solution

    |

  6. Let the funciton f:R to R be defined by f(x)=2x+sin x. Then, f is

    Text Solution

    |

  7. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  8. Let f :R->R be a function defined by f(x)=|x] for all x in R and let A...

    Text Solution

    |

  9. The function f:(-oo,-1)vec(0, e^5) defined by f(x)=e^x^(3-3x+2) is man...

    Text Solution

    |

  10. If the functions f, g and h are defined from the set of real numbers R...

    Text Solution

    |

  11. The distinct linear functions which map [-1, 1] onto [0, 2] are f(x...

    Text Solution

    |

  12. The values of a and b for which the map f: R to R, given by f(x)=ax+b(...

    Text Solution

    |

  13. Find the value of parameter alpha for which the function f(x)=1+alp...

    Text Solution

    |

  14. Let f:(2,oo)to X be defined by f(x)=4x-x^(2). Then f is invertible, if...

    Text Solution

    |

  15. If f:R->S defined by f(x)=sinx-sqrt(3)cosx+1 is onto , then the interv...

    Text Solution

    |

  16. If f(x)={{:(,|x|, x le1),(,2-x,x gt 1):}, then fof (x) is equal to

    Text Solution

    |

  17. Let A={x-1 le x le 1} and f:A to A such that f(x)=x|x| then f is:

    Text Solution

    |

  18. If f: R->(-1,\ 1) is defined by f(x)=(-x|x|)/(1+x^2) , then f^(-1)(x) ...

    Text Solution

    |

  19. Let f: R->R be given by f(x)=[x]^2+[x+1]-3 , where [x] denotes the gre...

    Text Solution

    |

  20. Let M be the set of all 2xx2 matrices with entries from the set R o...

    Text Solution

    |