Home
Class 12
MATHS
On the set of integers Z, define f : Z t...

On the set of integers Z, define f : `Z to Z` as
`f(n)={{:((n)/(2)",",,"n is even."),(0",",,"n is odd."):}`
Then, f is

A

injective but not surjective

B

neither injective nor surjectives

C

surjective but not injective

D

bijective

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 3: Composite Function and Relation, Inverse of a Function, Binary Operations)|27 Videos

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 1: Types of Relations, Inverse of a Relation)|14 Videos

  • RELATIONS AND FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE - 2|30 Videos

  • SEQUENCES AND SERIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

Let f : N to N : f (n) = {underset((n)/(2), " when n is even ")( (1)/(2) (n+1) , " when n is odd ") Then f is

Let N be the set of all natural numbers, Z be the set of all integers and sigma:N to Z defined by sigma (n) = {{:(n/2, "," "if n is even"),( - (n-1)/(2) , "," "if n is odd "):} then

Let z denote the set of all integers.Define : f:z rarr z by f(x)={(x)/(2),(xiseven),0,(xisodd) Then f is

A function f from the set of natural number to integers defined by f(n)={{:(,(n-1)/(2),"when n is odd"),(,-(n)/(2),"when n is even"):}

Let f:N to Z and f (x)=[{:((x-1)/(2),"when x is odd"),(-(x)/(2),"when x is even"):}, then:

A function f from integers to integers is defined as f(x)={{:(n+3",",nin"odd"),(n//2",",nin"even"):} suppose kin odd and f(f(f(k))) =27 then the sum of sigits of k is

If f:NrarrZ defined as f(n)={{:((n-1)/(2),":"," if n is odd"),((-n)/(2),":", " if n is even"):} and g:NrarrN defined as g(n)=n-(-1)^(n) , then fog is (where, N is the set of natural numbers and Z is the set of integers)

A function f from integers to integers is defined as f(n)={(n+3",",n in odd),(n//2 ",",n in even):} Suppose k in odd and f(f(f(k)))=27. Then the value of k is ________

DISHA PUBLICATION-RELATIONS AND FUNCTIONS-2-EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 2: Mappings, Mapping of Functions, Kinds of Mapping of Functions)
  1. Let f: R ,vecRw h e r ef(x)=(x^2+4x+7)/(x^2+x+1) . Is f(x)on eon e ?

    Text Solution

    |

  2. The set of parameter 'a' for which the functions f:R to R"defined by"f...

    Text Solution

    |

  3. If A= {1,3,5,7} and B= {1,2,3,4,5,6,7,8}, then the number of one-to-on...

    Text Solution

    |

  4. Which of the following is one-one function ?

    Text Solution

    |

  5. f:X to Y is onto, if and only if 1. range of f=Y 2. range of f neY ...

    Text Solution

    |

  6. Let A={1,2,..., n} and B={a , b }. Then number of subjections from A i...

    Text Solution

    |

  7. Let f: RtoR be function defined by f(x)=sin (2x-3), then f is

    Text Solution

    |

  8. On the set of integers Z, define f : Z to Z as f(n)={{:((n)/(2)",",,...

    Text Solution

    |

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

    Text Solution

    |

  10. If f : R -> R be a function such that f(x) = { x|x| -4; x in Q, x|x| -...

    Text Solution

    |

  11. Consider functions f and g such that composite gof is defined and is ...

    Text Solution

    |

  12. If f(x)=|x-2|, where x is a real number, then, which one of the follow...

    Text Solution

    |

  13. Let f : R - {n} rarr R be a function defined by f(x)=(x-m)/(x-n), wher...

    Text Solution

    |

  14. The function f : R -> R is defined by f (x) = (x-1) (x-2) (x-3) is

    Text Solution

    |

  15. Let A = {1, 2, 3) and B= {a,b,c}, and f= {(1, a),(2, b), (P, c)} be a...

    Text Solution

    |

  16. A function f: X to Y is said to be onto, if for every y in Y there ex...

    Text Solution

    |

  17. Let f be a one-one function with domain {x,y,z} and range {1,2,3}. It ...

    Text Solution

    |

  18. The mapping f : N to N given by f(n)=1+n^(2), n in N, where N is the s...

    Text Solution

    |

  19. The function f:R to R given by f(x)=x^(2)+x is

    Text Solution

    |