Home
Class 12
MATHS
Let S = {1, 2, 3}. Determine whether the...

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)}

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

Show that the function f:RtoR defined by f(x)=2x-3 is one-one and onto. Find f^-1

Let S={(1,2),(2,3),(3,4)}. Find S^-1

Let f : {1, 3, 4} rarr {1, 2, 5} and g : {1, 2, 5} rarr (1, 3} be given by f = {(1,2), (3,5), (4,1)} and g = {(1,3), (2,3), (5,1)} Write down g o f

A fuction f:RrarrR defined by f(x)=(2x-3)/7 . Find f^-1

State with reason whether the following functions have inverse f : {1,2,3,4} to {10} with f = {(1,10),(2,10),(3,10),(4,10)}

Determine whether the f(x)=x^3-x function is strictly monotonic on the indicated interval. (-1,(-1)/2)

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)}

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) .If invertible,find inverse of f(x).

If f: RrarrR be defined by f(x)=3x+2.Show that f is invertible.Find f^-1:RrarrR .Hence find f^-1(3) and f^-1(0)

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. ...

    Text Solution

    |

  2. Consider of f : N rarrN and h : N rarr R defined as f(x) = 2x, g(y) = ...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f : {1, 3, 4} rarr {1, 2, 5} and g : {1, 2, 5} rarr (1, 3} be gi...

    Text Solution

    |

  5. Let f, g, and h be functions from R to R. Show that (f + g) o h = fo...

    Text Solution

    |

  6. Find f o g and g o f f(x) = |x| and g(x) = |5x -2|

    Text Solution

    |

  7. If f(x) =(4x + 3)/(6x - 4), x ne 2/3, show that (fof)(x) = x, for all ...

    Text Solution

    |

  8. State with reason whether the following functions have inverse f : {...

    Text Solution

    |

  9. Show that f:[-1,1]toR given by f(x)=frac(x)(x+2) is one-one.

    Text Solution

    |

  10. Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. ...

    Text Solution

    |

  11. Consider f:R^+to[-5, infty) given by f(x)=9x^2+6x-5. Show that f is ...

    Text Solution

    |

  12. Let f : X rarr Y be invertible, show that f has unique inverse

    Text Solution

    |

  13. Consider f : {1, 2, 3} rarr {a, b, c} given by f(1) = a, f(2) = b and ...

    Text Solution

    |

  14. Let f : X rarr Y be invertible, show that the inverse of f^(-1) = f, ...

    Text Solution

    |

  15. If f : R rarr R be given by f(x) = (3 - x^3)^(1/3), then (f o f) (x) i...

    Text Solution

    |

  16. f : R - {(-4)/3} rarr R be a function defined as f(x) = (4x)/(3x +4). ...

    Text Solution

    |

  17. Can you define a function from 'RxR rarr R' such as 'f3: RxR rarr, R' ...

    Text Solution

    |

  18. Can yóu define a function from 'R xx R rarr R' such as 'f4: R xx R rar...

    Text Solution

    |

  19. Show that addition, subtraction and multiplication are binary opera...

    Text Solution

    |

  20. Show that subtraction and division are not binary operations on N.

    Text Solution

    |