Home
Class 12
MATHS
Let C be the set of complex numbers . Pr...

Let C be the set of complex numbers . Prove that the mapping `f : C rarr R ` given by `f(z) = |z| , AA z in C` , is neither one - one nor onto .

Text Solution

Verified by Experts

The correct Answer is:
f is not one - one function
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

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

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Objective type Questions)|20 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice Work|54 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 the function f : R rarr R be defined by f(x) = cos x , AA x in R . Show that f is nether one - one nor onto .

Let C and R denote the set of all complex numbers and all real numbers respectively. Then show that f: C->R given by f(z)=|z| for all z in C is neither one-one nor onto.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Prove that the function f :R rarr R , given by f(x) = 2x, is one-one and onto.

Show that the function f: R rarr R , defined as f(x) = x^2 , is neither one-one nor onto.

Give an example of a map Which is neither one - one nor onto.

If A = {0,1} and N be the set of natural numbers. Then , the mapping f: N rarr A defined by f(2n-1) = 0 , f(2n) = 1, AA n in N , is onto.

Show that the function f:N rarr N , given by f(x) = 2x, is one-one but not onto.

Show that the Signum Function f : R rarr R given by f(x) = {(1," if " x gt0),(0," if " x =0),(-1," if " x lt0):} is neither one - one nor onto.

Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1 , "if x is even"):} is both one - one and onto .

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Let A = {a,b,c} and the relation R be defined on A as follows : R = {...

    Text Solution

    |

  2. Let D be the domain of the real valued function f defined by f(x) = sq...

    Text Solution

    |

  3. If f,g : R rarr R be defined by f(x) = 2x + 1 and g(x) =x^(2) -2 , AA...

    Text Solution

    |

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

    Text Solution

    |

  5. If A = {a,b,c,d} and the function f ={(a,b),(b,d) , (c,a) ,(d,c) } . W...

    Text Solution

    |

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

    Text Solution

    |

  7. Is g= {(1, 1), (2,3), (3,5), (4,7)} a function, justify. If this is de...

    Text Solution

    |

  8. Are the following set of ordered pairs functions ? If so examine wheth...

    Text Solution

    |

  9. Are the following set of ordered pairs functions ? If so examine wheth...

    Text Solution

    |

  10. If the mappings f and g are given be f = {(1,2),(3,5),(4,1)} and g = {...

    Text Solution

    |

  11. Let C be the set of complex numbers . Prove that the mapping f : C rar...

    Text Solution

    |

  12. Let the function f : R rarr R be defined by f(x) = cos x , AA x in R ...

    Text Solution

    |

  13. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

    Text Solution

    |

  14. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

    Text Solution

    |

  15. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

    Text Solution

    |

  16. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

    Text Solution

    |

  17. If functions f : A rarr B and g : B rarr A satisfy gof = IA , then sho...

    Text Solution

    |

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

    Text Solution

    |

  19. Let n be a fixed positive integer. Defiene a relation R in Z as follow...

    Text Solution

    |