Home
Class 12
MATHS
Consider functions f and g such that com...

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

Text Solution

Verified by Experts

The correct Answer is:
gof is one-one but g is not clearly one-one
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

Are fand g both necessarily onto, if gof is onto?

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.

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| ) .

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 if f: A rarr B and g: B rarr C are one- one, then gof: A rarrC is also one-one.

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 .

Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) =x/(1+|x|),x in R is one one and onto function.

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

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.

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Show that if f: A rarr B and g: B rarr C are one- one, then gof: A ra...

    Text Solution

    |

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

    Text Solution

    |

  3. Consider functions f and g such that composite gof is defined and is o...

    Text Solution

    |

  4. Are fand g both necessarily onto, if gof is onto?

    Text Solution

    |

  5. Let f: {1, 2, 3} rarr {a,b,c} be one-one and onto function given by f...

    Text Solution

    |

  6. Let f:N rarr Y be a function defined as f(x) = 4x + 3, where, Y = { y...

    Text Solution

    |

  7. Let Y = {n^(2) :n in N} subN Consider f: N rarr Y as f(n) = n^2 . Sh...

    Text Solution

    |

  8. Let f':N rarr R be a function defined as f'(x) = 4x^(2) + 12x + 15 . ...

    Text Solution

    |

  9. Consider f: N rarr N,g :N rarr N and h: Nrarr R defined as f(x) = 2x, ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |