Home
Class 12
MATHS
Let S = {a,b,c} and T ={1,2,3}. Find F ^...

Let `S = {a,b,c} and T ={1,2,3}.` Find `F ^(-1)` of the following F from S to T, if exists.
(i) `F = {(a,3), (b,2), (c,1)}`
(ii) `F = {(a,2), (b,1), (c,1)}`

Text Solution

Verified by Experts

The correct Answer is:
`(i) F ^(-1) = {3,a) , (2,b) ,(1,c) } ,(ii) F ^(-1) ` does not exist
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.4|13 Videos
  • PROBABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos
  • VECTOR ALGEBRA

    NCERT BANGLISH|Exercise Miscellaneous Exercise on chapter 10|19 Videos

Similar Questions

Explore conceptually related problems

Let S = {1,2,3}. Determine whether the functions f : S to S defined as below have inverses. Find f ^(-1), if it exists. (a) f = {(1,1), (2,2), (3,3)} (b) f = {(1,2), (2,1),(3,1)} (c ) f { (1,3), (2,3),(2,1)}

Find the domain of the following functions (a) f(x)=(1)/(sqrt(x-2)) " (b) " f(x)=(1)/(x^(3)-x) (c ) f(x)= root(3)(x^(2)-2)

Let A ={a,b,c, d,e} and f: A rarr A be defined by f(a)=d, f (b) =a,f(c) =d, f(d) =b and f(e)=d find (i) f^(-1)(b) (ii) f^(-1) (e) (iii) f^(-1) (d) and (iv) f^(-1) {a,b} .

Let f(x)={1+(2x)/a ,0lt=x 1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

Let A={-1, 0, 1} and B = {1, 2, 3, 4}. If f is the rule associating elements of A to elements of B, such that f(-1) = 2, f(0) = 1 and f(1) = 4. Does f define a mapping?

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

Let A={x:-1 le x le 1}=B be a function f: A to B. Then find the nature of each of the following functions. (i) f(x) = |x| " (ii) " f(x)=x|x| (iii) f(x)=x^(3) " (iv) " f(x)="sin"(pi x)/(2)

Let A = {1,2,3},B ={4,5,6,7} and let f = {(1,4), (2,5), (3,6)} be function from A to B. Show that f is one-one.

Let f:{1,2,3} to {a,b,c} be one-one and onto function given by f (1) =a, f (2) =b and f (3) =c. Show that there exists a function g : {a,b,c} to {1,2,3} such that gof =I _(x) and fog =I _(y), where, X = {1,2,3} and Y={a,b,c}.

NCERT BANGLISH-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Let f : R to R be defined as f (x) =10 x +7. Find the function g : R t...

    Text Solution

    |

  2. Let f:Wto W be defined as f (n)=n -1, if n is odd and f (n) =n +1, if ...

    Text Solution

    |

  3. If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

    Text Solution

    |

  4. Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f...

    Text Solution

    |

  5. Show that the function f: R to R given by f (x) = x ^(3) is injective...

    Text Solution

    |

  6. Give examples of two functions f:N to Z and g: Z to Z such that g o f ...

    Text Solution

    |

  7. Give examples of two functions f : N to N and g : N to N such g o f is...

    Text Solution

    |

  8. Given a non empty set X, consider P (X) which is the set of all subset...

    Text Solution

    |

  9. Given a non-empty set X, consider the binary opertion **: P(X) xx P (Y...

    Text Solution

    |

  10. Find the number of all onto functins from the set {1,2,3..,n} to itsel...

    Text Solution

    |

  11. Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S...

    Text Solution

    |

  12. Show that +:R×R→R and o:R×R→R defined as a∗b=∣a−b∣ and aob=a for all a...

    Text Solution

    |

  13. Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as ...

    Text Solution

    |

  14. Define a binary opertion ** on the set {0,1,2,3,4,5} as a**b ={{:(a+...

    Text Solution

    |

  15. Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defin...

    Text Solution

    |

  16. Let A={1,2,3}. Then the number of relations containing (1,2) and (1,3)...

    Text Solution

    |

  17. Let A = {1,2,3},B={5,6.7} then find AcapB

    Text Solution

    |

  18. Let f: R → R be the Signum Function defined as f(x)={ 1, x>0 0, x=0−1,...

    Text Solution

    |

  19. Number of binary opertions on the set {a,b} are

    Text Solution

    |