Home
Class 11
MATHS
Let f be the subset of Z xxZdefined by f...

Let f be the subset of `Z xxZ`defined by `f = {(a b , a + b) : a , b in Z}`. Is f a function from Z to Z? Justify your answer.

Text Solution

Verified by Experts

The correct Answer is:
Is is not a function
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 2D|18 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 2E|5 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 2B|14 Videos

  • PROBABILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|10 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|32 Videos

Similar Questions

Explore conceptually related problems

Let R be the relation on Z defined by R = {(a , b): a , b in Z , a b is an integer}.Find the domain and range of R.

Let R be the relation on Z defined by R={(a , b): a , b in Z , a-b is an integer }dot Find the domain and range of Rdot

Check the commutativity of * on Z defined by a*b=a+b+a b for all a ,\ b in Z .

Let f = {(1, 2), (2, 3), (0, 1), ( -1, 0)} be a linear function from Z into Z. Find f(x).

Let R be the relation on Z defined by R={(a , b): a , b belongs to Z , a-b is an integer }dot Find the domain and range of Rdot

Show that the function f: ZvecZ defined by f(x)=x^2+x for all x in Z , is a many one function.

Determine whether O on Z defined by a\ O\ b=a^b for all a ,\ b in Z define a binary operation on the given set or not:

Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , is a function but not bijective function.

Let f be a function from R to R such that f(x)=cos(x+2) . Is f invertible? Justify your answer.

Let A = R - {3} and B = R - {1} . Consider the function f: A->B defined by (x)=((x-2)/(x-3)) . Is f one-one and onto? Justify your answer.

NAGEEN PRAKASHAN ENGLISH-RELATIONS AND FUNCTIONS-Exercise 2C
  1. Let f be the subset of Z xxZdefined by f = {(a b , a + b) : a , b in ...

    Text Solution

    |

  2. Examine each of the following relations given below and state in each...

    Text Solution

    |

  3. Let X = {1, 2, 3, 4, 5} and Y = {1, 3, 5, 7, 9}. Which of the followin...

    Text Solution

    |

  4. Let R be a relation defined on the set of natural numbers as: R={(x,...

    Text Solution

    |

  5. Express each relation in the form of ordered pair and check whether is...

    Text Solution

    |

  6. A function f: R to R is defined as: f(x) ={{:(1,x in Q),(-1,x notinQ...

    Text Solution

    |

  7. Find which of the following are the function on set A={a,b,c} ? Give r...

    Text Solution

    |

  8. A function f: R to R is defined asf(x)=x^(2)+1. Evaluate each of the f...

    Text Solution

    |

  9. If A={1,2,3,4},B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11...

    Text Solution

    |

  10. Let A = {9, 10 , 11 , 12 , 13}and let f : A ->Nbe defined by f(n) = th...

    Text Solution

    |

  11. If A={1,2} and B={3,6} and two functions f: A to B and g: A to B are d...

    Text Solution

    |

  12. Express the following functions in the form of order pairs and find th...

    Text Solution

    |

  13. If a function f:R to R is defined as f(x)=x^(2)+1, then find each of t...

    Text Solution

    |

  14. Let a function f:R^(+) to R is defined as f(x)="log"(e)x, then find ea...

    Text Solution

    |

  15. A function F(c) is defined as : F(c) =(9)/(5)*c+32. Evaluate each ...

    Text Solution

    |

  16. If f(x)=2x-5 , then evaluate the following: (i) f(0) (ii) f(7) (...

    Text Solution

    |

  17. If f(x)=x^(2), then evaluate: (f(1*2)-f(1))/(1*2-1)

    Text Solution

    |

  18. If f(x)=x^(2) , then evaluate : (f(x+1)-f(x-1))/(4x)

    Text Solution

    |

  19. If f(x)=(x)/(x-1), then evaluate : (f(a//b))/(f(b//a))

    Text Solution

    |

  20. If f(x)=(x-1)/(x+1), then prove that: (f(b)-f(a))/(1+f(b)*f(a))=(b-a...

    Text Solution

    |