Home
Class 12
MATHS
The function f:xtoY defined by f(x)=x^(2...

The function `f:xtoY` defined by `f(x)=x^(2)-4x+5` is both one-one and onto if

A

`T =R`

B

`Y = [1,oo]`

C

`Y = [4,oo)`

D

`Y = [ 5, oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    MOTION|Exercise Exercise - 2 (Level-I)|33 Videos

  • FUNCTION

    MOTION|Exercise Exercise - 2 (Level-II)|6 Videos

  • FUNCTION

    MOTION|Exercise Exercise - 4 | Level-II|7 Videos

  • ELLIPSE

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|20 Videos

  • HYPERBOLA

    MOTION|Exercise EXERCISE-4 (Level-II)|17 Videos

Similar Questions

Explore conceptually related problems

The function f:[2,oo)rarr Y defined by f(x)=x^(2)-4x+5 is both one-one and onto if

The function f:XtoY defined by f(x)=cosx where x""inX , is one-one and onto if X and Y are respectively equal to

Show that the function f:RrarrR defined by f(x)=x^(2) is neither one-one nor onto.

The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and onto (b) many-one and onto (c) one-one and into (d) many-one and into

The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and onto (b) many one and onto (c) one-one and into (d) many one and into

The function f:XtoY defined by f(x)=sinx is one-one but not onto, iff X and Y are respectively equal to

Show that the function f:R rarr R defined by f(x)=x^4+5 is neither one one nor onto

Prove that the function f:N rarr N, defined by f(x)=x^(2)+x+1 is one-one but not onto

Show that the function f:R rarr R defined as f(x)=x^(2) is neither one-one nor onto.

Prove that the function F:N rarr N, defined by f(x)=x^(2)+x+1 is one-one but not onto.

MOTION-FUNCTION-Exercise - 1 ( JEE Main)
  1. Let A={p,q,r} and B={1,2}. Represent (i) A x B (ii) B x B

    Text Solution

    |

  2. If A={-3,3), form the set A x A x A

    Text Solution

    |

  3. The function f:xtoY defined by f(x)=x^(2)-4x+5 is both one-one and ont...

    Text Solution

    |

  4. Let f: RrarrR be a function defined by f(x)=(2x^2-x+5)/(7x^2+2x+10) th...

    Text Solution

    |

  5. Let f :RrarrR be a function defined by f(x) = x^3 + x^2 + 3x + sin x. ...

    Text Solution

    |

  6. If f(x) = (4a-7)/3 x^3+(a-3)x^2 +x+5 is one-one function

    Text Solution

    |

  7. The function f : (-oo, 3] to (o,e ^(7)] defined by f (x)=e ^(x^(3)-3x^...

    Text Solution

    |

  8. f : R -> R, where f(x)=(x^2+ax+1)/(x^2+x+1) Complete set of values of ...

    Text Solution

    |

  9. The function f(x)=log((1+sinx)/(1-sinx)) is

    Text Solution

    |

  10. It is given that f(x) is an even function and satisfy the relation f(x...

    Text Solution

    |

  11. If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx ,...

    Text Solution

    |

  12. Let f(x)=abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4), then

    Text Solution

    |

  13. Fundamental period of f(x)=sec(sin x) is

    Text Solution

    |

  14. The period of sin(pi/4)x+cos(pi/2)x+cos(pi/3)x is

    Text Solution

    |

  15. Let f(x)=x(2-x), 0<=x<=2. If the definition of f is extended over the ...

    Text Solution

    |

  16. The peroid of the function f(x) =(|sinx|-|cosx|)/(|sin x + cosx|) i...

    Text Solution

    |

  17. Which of the following is implicit functions -

    Text Solution

    |

  18. I fy=f(x) satisfies the condition f(x+1/x)=x^2+1/(x^2)(x!=0) then f(x...

    Text Solution

    |

  19. If f(x) = a(x^n +3), f(1) = 12, f(3) = 36, then f(2) is equal to

    Text Solution

    |

  20. Let f:(2,4)->(1,3) be a function defined by f(x)=x-[x/2], thenf^(-1)(x...

    Text Solution

    |