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

Let S = {1, 2, 3}. Determine whether the functions `f:S rarr S` defined as below have inverses. Find `f^(-1)`, if it exists.
Note : Here we accept that inverse at function is unique.
` f = {(1, 1), (2, 2), (3, 3)}`

Text Solution

Verified by Experts

The correct Answer is:
Inverse of f exists and `f^(-1) = {(1, 1), (2, 2), (3, 3)} = f`.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|19 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|30 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|64 Videos

  • PROBABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 13 (Section - D (Answer the following questions))|2 Videos

  • THREE DIMENSIONAL GEOMETRY

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER -11|16 Videos

Similar Questions

Explore conceptually related problems

Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined as below have inverses. Find f^(-1) , if it exists. Note : Here we accept that inverse at function is unique. f = {(1, 3), (3, 2), (2, 1)}

Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined as below have inverses. Find f^(-1) , if it exists. Note : Here we accept that inverse at function is unique. f = {(1, 2), (2, 1), (3, 1)}

Let A = [-1,1] . Then , discuss whether the following functions defined on A are one - one , onto or bijective. f(x) =x/2

Find the range and domain of the function defined by f(x)= (1)/(2- sin 3x)

If the function f:[1, infty) rarr [1, infty) is defined by f(x)=2^(x(x-1)) , then find f^(-1)(x) .

Let f : X rarr Y be an invertible function . Show that the inverse of f^(-1) is f . i.e., (f^(-1))^(-1)= f .

Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be onto.

Let A = R - {3} and B = R - {1}. Consider the function f : A rarrB defined by , f(x) = ((x-2)/(x-3)) is f one - one and onto ?

Let f: X -> Y be an invertible function. Show that the inverse of f^(-1) is f, i.e., (f^(-1))^(-1)= f .

Let f : R rarr R be the function defined by f(x) = 2x - 2 , AA x in R . Write f^(-1) .

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Consider f: N rarr N,g :N rarr N and h: Nrarr R defined as f(x) = 2x, ...

    Text Solution

    |

  2. Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} de...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Show that addition, subtraction and multiplication are binary operatio...

    Text Solution

    |

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

    Text Solution

    |

  8. Show that ** :Rxx R rarr R given by (a, b) rarr a + 4b^(2) is a bina...

    Text Solution

    |

  9. Let P be the set of all subsets of a given set X. Show that cup: P xxP...

    Text Solution

    |

  10. Show that the VV: RxxR rarr R given by (a, b) rarr max {a, b} and th...

    Text Solution

    |

  11. Show that + : Rxx R rarr R and xx: R xxR rarr R are commutative binar...

    Text Solution

    |

  12. Show that **: RxxR rarr R defined by a^(**) b = a + 2b is not commuta...

    Text Solution

    |

  13. Show that addition and multiplication are associative binary operation...

    Text Solution

    |

  14. Show that ""^** : R xxR rarr R given by a^** b rarr a + 2b is not ass...

    Text Solution

    |

  15. Show that zero is the identity for addition on R and 1 is the identity...

    Text Solution

    |

  16. Show that -a is the inverse of a for the addition operation '+' on R...

    Text Solution

    |

  17. Show that -a is not the inverse of a in N for the addition operation...

    Text Solution

    |

  18. If R1 and R2 are equivalence relations in a set A, show that R(1) cap...

    Text Solution

    |

  19. Let R be a relation on the set A of ordered pairs of positive integers...

    Text Solution

    |

  20. Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let R1 be a relation in X given ...

    Text Solution

    |