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

On the set Z of all integers define `f : Z-(0) rarr Z` as follows
`f(n)= {(n/2, n \ is \ even) , (2/0 , n \ is \ odd):}` then f is

A

onto but not one-one

B

one-one but not onto

C

one-one and onto

D

into

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS AND EXPRESSION

    HIMALAYA PUBLICATION|Exercise Question Bank|129 Videos

  • STATISTICS MEASURE OF DIPERSION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|28 Videos

Similar Questions

Explore conceptually related problems

Let f:N rarr N defined by f(n)={{:((n+1)/(2) " if n is odd"),(n/2" if n is even"):} then f is

Let I be the set of integer and f : I rarr I be defined as f(x) = x^(2), x in I , the function is

On the set Z , of all integers ** is defined by a^(**)b=a+b-5 . If 2^(**)(x^(**)3)=5 then x=

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

Let R be a relation on the set Z of all integers defined by:(x,y) in R implies(x-y) is divisible by n.Prove that (b) (x,y) in R implies(y,x) in R for all x,y,z in Z .

Let R be a relation on the set Z of all integers defined by:(x,y) in R implies(x-y) is divisible by n is eqivalence

Prove that 2^(n) gt n for all positive integers n.

Let f: N rarr N be defined by f(x)=x^(2)+x+1 then f is

If f(x) = (a-x^n)^1/n, a gt 0 , n is a postive integer then f[f(x)]=

HIMALAYA PUBLICATION-SETS,RELATIONS AND FUNCTIONS-QUESTION BANK
  1. If g(x) = 1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) =

    Text Solution

    |

  2. The inverse of the function f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x))+2 is gi...

    Text Solution

    |

  3. On the set Z of all integers define f : Z-(0) rarr Z as follows f(n)...

    Text Solution

    |

  4. The mapping f:R^+ rarr R defined by f(x) = log{10}x, (Where R^+ is the...

    Text Solution

    |

  5. The function f(x) = 10^x from the set R of real numbers to [0,oo) is

    Text Solution

    |

  6. If R denotes the set of all real numbers than the function f : R rarr ...

    Text Solution

    |

  7. If f : N xx N rarr N is such that f (m,n) = m+n, for all n in N, where...

    Text Solution

    |

  8. If f(x)=(2^(x)-2^(-x))/(2^(x)+2^(-x)),"then"f^(-1)(x) is :

    Text Solution

    |

  9. If f(x) = (1-x)/(1+x), then f[f(cos x)]=

    Text Solution

    |

  10. If f(x) = (x-3)/(x+1), then f[f{f(x)}]=

    Text Solution

    |

  11. If f(x) = x/(x - 1) = 1/y, then f(y)=

    Text Solution

    |

  12. If f(x) = (x-1)/(x+1), then f[1/f(x)]=

    Text Solution

    |

  13. The number of bijective functions from the set A to itself, if A conta...

    Text Solution

    |

  14. If f: R rarr R be defined by , f(x) = 10x - 7 and g = f^-1, then g(x...

    Text Solution

    |

  15. Let A be a set containing 10 distinct elements . Then the total number...

    Text Solution

    |

  16. If the set A has 3 elements and the set B has 4 elements, then the nu...

    Text Solution

    |

  17. The number of bijective functions from the set A to itself if a contai...

    Text Solution

    |

  18. If f(x)=(3x+2)/(5x-3), then :

    Text Solution

    |

  19. If f(x) = 4x - x^2, then f (a + 1) - f( a - 1) =

    Text Solution

    |

  20. If f(x) = 1 - 1/x, then f(f(1/x)) =

    Text Solution

    |