Home
Class 12
MATHS
The function f: A->B defined by f(x)=-x^...

The function `f: A->B` defined by `f(x)=-x^2+6x-8` is a bijection, if `A=(-oo,\ 3]` and `B=(-oo,\ 1]` (b) `A=[-3,\ oo)` and `B=(-oo,\ 1]` (c) `A=(-oo,\ 3]` and `B=[1,\ oo)` (d) `A=[3,\ oo)` and `B=[1,\ oo)`

Text Solution

Verified by Experts

`A=(-infty, 3]` and `B=(-infty, 1]`

`f(x)=-x^{2}+6 x-8`, is a polynomial function

And the domain of polynomial function is real number.

`therefore x in R`

`f(x)=-x^{2}+6 x-8 `

...
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos
  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

If a funciton f:[2,oo] to B defined by f(x)=x^(2)-4x+5 is a bijection, then B=

The function defined by f(x)={x^(3)-1;1

If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^(-1) is

If the function f:[2,oo)rarr[-1,oo) is defined by f(x)=x^(2)-4x+3 then f^(-1)(x)=

f:(-oo,oo)rarr(-oo,oo) defined by f(x)=|x| is

If the function, f:[1,oo]to [1,oo] is defined by f(x)=3^(x(x-1)) , then f^(-1)(x) is

The domain of the function f:R rarr R defined by f(x)=sqrt(x^(2)-3x+2) is (-oo,a]uu[b,oo) then b-a

Let a function f:(1, oo)rarr(0, oo) be defined by f(x)=|1-(1)/(x)| . Then f is

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and on...

    Text Solution

    |

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

    Text Solution

    |

  3. The function f: A->B defined by f(x)=-x^2+6x-8 is a bijection, if A=(-...

    Text Solution

    |

  4. Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and on...

    Text Solution

    |

  8. The range of the function f(x)=\ ^(7-x)P(x-3) is (a) {1, 2, 3, 4, ...

    Text Solution

    |

  9. A function f from the set of natural numbers to integers is defined by...

    Text Solution

    |

  10. Let f be an injective map. with domain (x, y, z and range (1, 2, 3), s...

    Text Solution

    |

  11. Which of the following function from Z to itself are bijections? f(x)=...

    Text Solution

    |

  12. Let A=[-1,1]dot Then, discuss whether the following functions from A t...

    Text Solution

    |

  13. Let A}x :-1lt=xlt=1}a n df: Avec such that f(x)=x|x|, then f is a bije...

    Text Solution

    |

  14. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

    Text Solution

    |

  15. If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one...

    Text Solution

    |

  16. The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=sin^(-...

    Text Solution

    |

  17. Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(...

    Text Solution

    |

  18. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!...

    Text Solution

    |

  19. Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is...

    Text Solution

    |

  20. f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-on...

    Text Solution

    |