Home
Class 12
MATHS
Prove that for any f:X rarr Y , f o idx ...

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

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 B sube Y, f(f^(-1)(B)) =B.

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

Determine whether the function f:X rarr Y defined by f(x) = 4x + 7, x in X is one-one.

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.

Let f:XrarrY . If there exists a map g:YrarrX such that g of= id_x and fo g= id_y then show that g=f^(-1)

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) .

Show that the function f: R rarr R , f(x)= x^(4) is many-one and into.

State whether the function f : R rarr R, defined by f(x) = 3 - 4x is onto or not.

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

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the feasible solution region of the following: 3x+yge3,x+yge1,xge...

    Text Solution

    |

  2. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

    Text Solution

    |

  3. Prove that for any f:X rarr Y , f o idx = f =idY of.

    Text Solution

    |

  4. If A=[(2,5),(1,3)], then find A^(-1)

    Text Solution

    |

  5. Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,...

    Text Solution

    |

  6. If [(x+y,y-z),(5-t,7+x)]=[(t-x,z-t),(z-y,x+z+t)], then find the values...

    Text Solution

    |

  7. Express as a sum of a symmetric and a skew symmetric matrix: [[1,2,3],...

    Text Solution

    |

  8. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

    Text Solution

    |

  9. Find the intervals where the following functions are (a) increasing an...

    Text Solution

    |

  10. Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).

    Text Solution

    |

  11. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

    Text Solution

    |

  12. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

    Text Solution

    |

  13. Let f(x)={(absx/x,if xne0),(0,if x=0):} Examine the continuity of f(x)...

    Text Solution

    |

  14. int(1+x^2)/(xsqrt(x^4+1))dx

    Text Solution

    |

  15. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

    Text Solution

    |

  16. int0^pi(xsinxdx)/(1+cos^2x)

    Text Solution

    |

  17. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

    Text Solution

    |

  18. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

    Text Solution

    |

  19. Prove that the sum of the vectors directed from the vertices to the mi...

    Text Solution

    |

  20. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

    Text Solution

    |