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

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

Text Solution

Verified by Experts

i) .F^(-1)(3 , a)(2, b)(1, c).
(ii) .F^(-1). does not exist
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|132 Videos

  • THREE DIMENSIONAL GEOMETRY

    V PUBLICATION|Exercise QUESTION BANK|103 Videos

Similar Questions

Explore conceptually related problems

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

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

Let S = {1, 2, 3}. Determine whether the function f : S rarr 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), (3,2), (2,1)}

Let f = {(1,1), (2,3),(0, -1), (- 1, - 3)} be a function from Z to Z defined by f (x) = ax + b , for some integers a,b. determine a,b.

If A = {1,2,3} and f is a relation on A defined as follows, then find the given relation is a function or not from A to A ? Explain f = {(1,2),(3,2)}

Let A=R-{3} and B=R-{1} consider the function f:ArarrB defined by f(x)=(x-2)/(x-3) .Is it invertible?Why?

Let A = {1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5),(2,9),(3,1),(4,5),(2,11),}. Are the following true? F is a function from A to B. Justify your answer.

Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Find A^T and B^T

Let f and g be two real functions defined by f(x)=1/(x+4) and g(x)=(x+4)^3 , find the following: i) f-g ii) f/g iii) 2f

The number of linear functions f satisfying f(x+f(x))= x + f (x) AA x in R is a)0 b)1 c)2 d)3

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

    Text Solution

    |

  2. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Find the number of all onto functions from the set {1,2,3 …... n}to i...

    Text Solution

    |

  7. Let S={a, b, c} and T={1,2,3}, Find F^-1 of the following functions F ...

    Text Solution

    |

  8. Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions define...

    Text Solution

    |

  9. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)20 ...

    Text Solution

    |

  10. Show that the relation R on the set N xx N defined by (a, b)R(c, d)...

    Text Solution

    |

  11. If f: R rarr R be a function defined by f(x)=4 x^3-7, show that the fu...

    Text Solution

    |

  12. Consider the binary operation ast : QtoQ where Q is the set of rationa...

    Text Solution

    |

  13. Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q...

    Text Solution

    |

  14. Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-...

    Text Solution

    |

  15. Let f: R rarr R be a function defined by f(x)=x^2-3 x+2 Find f^' (2) a...

    Text Solution

    |

  16. If f : R rarrR be defined by f(x) = 5x - 3, then prove that f is one-o...

    Text Solution

    |

  17. Let f, g: R rarr R be defined by f(x)=x^2+1and g(x)=sin x. Find f o g ...

    Text Solution

    |

  18. If f, g: R rarr R are defined by f(x)=x^2+3 x+1, g(x)=2 x-3, find (i) ...

    Text Solution

    |

  19. Let * be a binary operation on N, the set of all natural numbers defin...

    Text Solution

    |

  20. Let A=N xx N and let * be a binary operation on A defined by (a, b)*(...

    Text Solution

    |