Home
Class 12
MATHS
Which of the following functions from Z ...

Which of the following functions from Z to itself are bijections? a

A

`f(x)=x^(3)`

B

`f(x)=x+2`

C

`f(x)=2x+1`

D

`f(x)=x^(2) +1`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `f(x) =x +2impliesf(x_(1))=f(x_(2))`
`x_(1)+2=x_(2)+2implies x_(1)=x_(2)`
Let `" " y=x+2`
`x=y-2 in Z, AA y in x`
Hence, f(x) is one-one and onto.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    NCERT EXEMPLAR|Exercise Probability|107 Videos

  • THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Three Dimensional Geometry|46 Videos

Similar Questions

Explore conceptually related problems

Which of the following functions from l to itself are bijections?

Which of the following function from Z to itself are bijections? f(x)=x^(3)( b) f(x)=x+2f(x)=2x+1( d )f(x)=x^(2)+x

Let A = [-1, 1]. Which of the following functions on A is not a bijection?

If A={1,2,3,4} , then which of the following are functions from A to itself?

Which of the following functions is inverse of itself?

Let A=[-1,1]. Then,discuss whether the following functions from A to itself are one-one onto or bijective: f(x)=(x)/(2) (ii) g(x)=|x|quad (iii) h(x)=x^(2)

NCERT EXEMPLAR-RELATIONS AND FUNCTIONS-Relations And Functions
  1. If f: R to R be defined by f(x) =(1)/(x), AA x in R. Then , f is

    Text Solution

    |

  2. If f:R to R be defined by f(x)=3x^(2)-5 and g: R to R by g(x)= (x)/(x...

    Text Solution

    |

  3. Which of the following functions from Z to itself are bijections? a

    Text Solution

    |

  4. f:R->R defined by f(x) = x^2+5

    Text Solution

    |

  5. If f:A to B and g:B to C be the bijective functions, then (gof)^(-1) i...

    Text Solution

    |

  6. Let f: R-{3/5}->R be defined by f(x)=(3x+2)/(5x-3) . Then

    Text Solution

    |

  7. If f(x) is defined on [0, 1] by the rule f(x)={x, if x is ration...

    Text Solution

    |

  8. If f : [2,oo) to R be the function defined by f(x)=x^(2)-4x+5, then th...

    Text Solution

    |

  9. Let f:N rarr R be the function defined by f(x)=(2x-1)/2 and g:Q rarr Q...

    Text Solution

    |

  10. If f: R to R be defined by f(x)={(2x:xgt3),(x^(2):1lt x le 3),(3x:x le...

    Text Solution

    |

  11. If f:R to R be given by f(x)= tan x, then f^(-1)(1) is

    Text Solution

    |

  12. Let the relation R be defined in N by a R b, if 2a + 3b = 30. Then R =...

    Text Solution

    |

  13. If the relation R be defined on the set A={1,2,3,4,5} by R={(a,b): |a^...

    Text Solution

    |

  14. If the functions f and g are given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} ...

    Text Solution

    |

  15. If f:R to R be defined by f(x) = (x)/(sqrt(1 +x^(2) )), then (fofof)...

    Text Solution

    |

  16. If f(x) = [4-(x-7)^(3)], then f^(-1)(x)= ………… .

    Text Solution

    |

  17. State true or false for the given statement : Let R = { (3, 1), (1,...

    Text Solution

    |

  18. If f:R to R be the function defined by f(x) = sin(3x+2) AA x in R. Th...

    Text Solution

    |

  19. Every relation which is symmetric and transitive is also reflexive.

    Text Solution

    |

  20. An integer m is said to be related to another integer n if m is a m...

    Text Solution

    |