Home
Class 12
MATHS
Prove that f:X rarr Y is injective iff f...

Prove that `f:X rarr Y` is injective iff `f^(-1) (f(A)) = "A for all" A sube X`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

Prove that f: X rarr Y is surjective iff for all A sube X,(f(A))' sube f(A') , where A' denotes the complement of A in X.

Prove that f:X rarr Y is injective iff for all subsets A,B of X,f(A nn B ) = f(A) nn f(B) .

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

Prove that f:X to Y is injective iff for all subsets A, B of X, f (A cap B) =f(A) cap f(B) .

If f:XrightarrowY is onto, then prove that f(f^(-1)(B))=B for all BsubseteqY .

Prove that for any f:X rarr Y , f o id_x = f =id_Y of.

Consider f : R rarr (-9 ,oo) given by f(x) = 5x^(2)+ 6x-9 . Prove that f is invertible with f^(-1) (y) = ((sqrt(54+5y)-3)/(5)) where R^(+) is the set of all positive real numbers.

Show that the function f: N rarr N, given by f(1) f(2)= 1 and f(x) = x - 1 for every x gt 2, is onto but not one-one.

Prove that f(x)=|x| is not differetiable at x=0

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve xfrac[dy][dx]+y=x^4

    Text Solution

    |

  2. If f:XrightarrowY is onto, then prove that f(f^(-1)(B))=B for all Bsub...

    Text Solution

    |

  3. Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...

    Text Solution

    |

  4. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

    Text Solution

    |

  5. Prove that the measure of the angle between two main diagonals of a cu...

    Text Solution

    |

  6. Show that the shortest distance between the lines x+a=2y=-12z and x=y+...

    Text Solution

    |

  7. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

    Text Solution

    |

  8. Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...

    Text Solution

    |

  9. Shows that the triangle of greatest area that can be inscribed in a ci...

    Text Solution

    |

  10. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

    Text Solution

    |

  11. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

    Text Solution

    |

  12. If A [[1,2,0],[1,1,0],[-1,4,0]],B=[[1,2,3],[1,1,-1],[1,1,1]]"and"C=[[1...

    Text Solution

    |

  13. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

    Text Solution

    |

  14. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

    Text Solution

    |

  15. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

    Text Solution

    |

  16. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

    Text Solution

    |

  17. Find the number of binary operations on the set {a,b}.

    Text Solution

    |

  18. If A, B are symmetric matrices of same order, then find AB-BA.

    Text Solution

    |

  19. Let A be square matrix of order 3times3, then find abs(KA) where, k is...

    Text Solution

    |

  20. If A is an invertible matrix of order 2, then find det(A^(-1)).

    Text Solution

    |