Home
Class 12
MATHS
Examine f:(-1,1) rarr R,f(x) = x/(1-x^2f...

Examine` f:(-1,1) rarr R,f(x) = x/(1-x^2`functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MODERN PUBLICATION|Exercise PROBLEM|18 Videos

  • SAMPLE PAPER 2012

    MODERN PUBLICATION|Exercise EXERCISE|37 Videos

Similar Questions

Explore conceptually related problems

Examine f :R rarr R, f(x) =x^2 functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Examine f:R rarr R ,f(x) =x^3 +1 functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Examine f:R rarr R, f(x) =|x| functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Examine f: R rarr R, f(x) ="sgn" x functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Examine f:R rarr [-1,1],f(x) = sin x functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Examine f:R_+ rarr R +, f(x) =x +1/x "where"R_+={x in R :x gt 0} functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Examine f:R rarr R, f(x) = [x] ="the greatest integer" le x. functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Examine f:R rarr R, f = id _R="the identity function or R." functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

Show that f(x)=sin x on [0, pi/2] functions are injective.

Show that the function f(x)=a^(x), x in R is injective, where (a gt 0 and a ne 1) .

MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

    Text Solution

    |

  2. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

    Text Solution

    |

  3. Let * is a binary operation on the set of all non-zero real numbers, g...

    Text Solution

    |

  4. Test whether the relations are reflexive, symmetric or transitive on t...

    Text Solution

    |

  5. Suppose a box contains a set of n balls (n gt 4)(denoted by B )of four...

    Text Solution

    |

  6. If f:XtoY and g:YtoZ be two bijective functions, then prove that (gof)...

    Text Solution

    |

  7. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

    Text Solution

    |

  8. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

    Text Solution

    |

  9. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

    Text Solution

    |

  10. Examine f:(-1,1) rarr R,f(x) = x/(1-x^2functions if it is (i) injecti...

    Text Solution

    |

  11. Consider f:R(+) [4, oo] is given by f(x)= x^(2) + 4. Show that f is in...

    Text Solution

    |

  12. Test whether the relations are reflexive, symmetric or transitive on t...

    Text Solution

    |

  13. Find the number of equivalence, relations on X ={1,2,3),

    Text Solution

    |

  14. Let A = {1, 2, 3). Then, show that the number of relations containing ...

    Text Solution

    |

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

    Text Solution

    |

  16. Show that f : N to N, given by f(x)= {(x+1", if x is odd"),(x-1", if...

    Text Solution

    |

  17. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

    Text Solution

    |

  18. Congruence modulo 3 relation partitions the set Z into how many equiva...

    Text Solution

    |

  19. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  20. Constract the composition table/multiplication table for the binary op...

    Text Solution

    |