Home
Class 12
MATHS
Xa n dY are two sets and f: XvecYdot If ...

`Xa n dY` are two sets and `f: XvecYdot` If `{f(c)=y ; csubX ,ysubY}a n d{f^(-1)(d)=x ; dsubY ,xsubX",` then the true statement is `f(f^(-1)(b))=b` (b) `f^(-1)(f(a))=a` `f(f^(-1)(b))=b , bsuby` (d) `f^(-1)(f(a))=a , asubx`

A

`f{f^(-1)(b))=b`

B

`f^(-1)(f(a))=a`

C

`f(f^(-1)(b))=b,bsubsety`

D

`f^(-1)(f(a))=a,asubsetx`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-II|20 Videos

  • FUNCTION

    FIITJEE|Exercise COMPREHENSIONS|8 Videos

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-II|17 Videos

  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

Similar Questions

Explore conceptually related problems

X and Y are two sets and f:X rarr Y If {f(c)=y;c sub X,y sub Y} and {f^(-1)(d)=x;d sub Y,x sub X, then the true statement is (a)f(f^(-1)(b))=b (b)f ^(-1)(f(a))=a(c)f(f^(-1)(b))=b,b sub y(d)f^(-1)(f(a))=a,a sub x

f(x)=(x)/(x-1) then (f(a))/(f(a+1)) is equal to a.f(-a) b.f(1/a) c.f(a^(2)) d.f (-(a)/(a-1))

If f(x)=(x-1)/(x+1) , then prove that: (f(b)-f(a))/(1+f(b)*f(a))=(b-a)/(1+ab)

If f(x)=|(log)_(e)x|, then (a) f'(1^(+))=1 (b) f'(1^(-))=-1( c) f'(1)=1(d)f'(1)=-1

int_(a)^(b-a)f''(x+a)dx equals (a) f(b-a)-f(a) " " (b) f(b)-f(2a) (c) f'(b)-f'(2a) " " (d) f'(b-a)-f'(2a)

If f(x)=(x)/(x-1) , then evaluate : (f(a//b))/(f(b//a))

If f(x)=|(log)_(2)x|, then f(1^(+))=1 (b) f(1^(-))=-1f(1)=1( c) f'(1)=-1

If f is continuous on [a,b] and differentiable in (a,b) then there exists c in(a,b) such that (f(b)-f(a))/((1)/(b)-(1)/(a)) is

If f((ax+b)/(x-a))=x, then f^(-1)(x)= (a) x (b) (bx+a)/(x-b)( c) f(x)

FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (OBJECTIVE) Level-I
  1. If f(x)=abs(x-1)+abs(x-4)+abs(x-9)+…+abs(x-2500)AA x inR, where m and ...

    Text Solution

    |

  2. Domain of the function f(x) = sin^(-1) [1 + cos x]- sqrt(16-x^(2)) ([....

    Text Solution

    |

  3. The number of solutions of log(x)3. = 2x-3 is,

    Text Solution

    |

  4. Domain of f(x)=sqrt((x-1)/(x-2{x})), where {.} denotes the fractional ...

    Text Solution

    |

  5. Let f(x)=sqrt([sin 2x] -[cos 2x]) (where I I denotes the greatest inte...

    Text Solution

    |

  6. The region M consists of all the points (x, y) satisfying the inequali...

    Text Solution

    |

  7. The domain of the function f(x)=sqrt(((sinx-e^(x))(cosx-3)("In"x+2))/(...

    Text Solution

    |

  8. A function f: I to I, f(x + y) = f(x) + f(y) - 1/2 AAx, y in I, where ...

    Text Solution

    |

  9. Consider the function f: A -> A where A:{1,2,3,4,5} which satisfy the...

    Text Solution

    |

  10. If f(x+y)=f(x)-f(y)+2xy-1AAx,yinR. Also if f(x) is differentiable and ...

    Text Solution

    |

  11. If f(x) is a real-valued function discontinuous at all integral points...

    Text Solution

    |

  12. A function f from integers to integers is defined as f(x)={{:(n+3",",n...

    Text Solution

    |

  13. f(x)+f(1-1/x)=1+x for x in R-{0,1}. Find the value of 4f(2).

    Text Solution

    |

  14. Xa n dY are two sets and f: XvecYdot If {f(c)=y ; csubX ,ysubY}a n d{f...

    Text Solution

    |

  15. The range of the function f(x) = sqrt(4 - x^2) + sqrt(x^2 - 1) is

    Text Solution

    |

  16. The domain function f(x) = 1/ (sqrt((|sin^-1x|-cos^-1|x|))) is given b...

    Text Solution

    |

  17. If f(x)=abs(1/(abs(absx-2))+1/(abs(absx-3))) and g(x)=sin^(-1)(2sqrtx)...

    Text Solution

    |

  18. If a function satisfies the condition f(x+1/x)=x^(2)+1/(x^(2)),xne0, t...

    Text Solution

    |

  19. Statement -1: f(x) is invertible function and f(f(x)) = x AA x in doma...

    Text Solution

    |

  20. If log(4)(x+2y)+log(4)(x-2y)=1, then Statement-1: (|x|-|y|)(min)=sqr...

    Text Solution

    |