Home
Class 12
MATHS
Give examples of two functions f:N rarr ...

Give examples of two functions `f:N rarr Z and g: Z rarr Z` such that gof is injective but g is not injective.
(Hint : Consider f(x) = x and g(x) = |x| ) .

Text Solution

Verified by Experts

The correct Answer is:
gof is injective but g is not injective.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Practice Work|66 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|64 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise EXERCISE 1.4|25 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

Give examples of two function f: N rarr N and g : N rarr N such that gof is onto but f is not onto. (Hint: Consider f(x) = x+1 " and "g(x) = {x-1 if x>1 1 if x=1.

Find gof and fog , if f (x) = |x| and g(x) = |5x-2| .

For functions f: A rarr B and g : B rarr A , gof = I_A . Prove that f is one one and g onto functions .

If functions f : A rarr B and g : B rarr A satisfy gof = I_A , then show that f is one one and g is onto.

Find gof and fog , if f(x) = 8x^(3) and g(x) =x^(1/3)

If f : A rarr B and g : B rarr C be the bijective functions , then (gof)^(-1) is ..........

Show that if f: A rarr B and g: B rarr C are onto, then gof: A rarr C is also onto.

Consider functions f and g such that composite gof is defined and is oneone. Are f and g both necessarily one-one.

Let f: RvecRa n dg: RvecR be two given functions such that f is injective and g is surjective. Then which of the following is injective? gof (b) fog (c) gog (d) none of these

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

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -MISCELLANEOUS EXERCISE - 1
  1. Let f : R rarr R be defined as f(x) = 10 x +7. Find the function g:R r...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) ...

    Text Solution

    |

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

    Text Solution

    |

  6. Give examples of two functions f:N rarr Z and g: Z rarr Z such that go...

    Text Solution

    |

  7. Give examples of two function f: N rarr N and g : N rarr N such that g...

    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 operation ** : P(X) x...

    Text Solution

    |

  10. Find the number of all onto functions from the set {1,2,3,.......,n} t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Consider the binary operations ** R xx R rarrR and o : RxxR rarrR defi...

    Text Solution

    |

  14. Given a non - empty set X , let **:P(X) xxP(X) rarr P(X) be defined ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Let A = {1,2,3}. Then number of equivalence relations containing (1,2)...

    Text Solution

    |

  19. Let f : R rarr R be the Signum Function defined as f(x) = {(1,xgt0),(...

    Text Solution

    |

  20. Number of binary operations on the set {a,b} are

    Text Solution

    |