Home
Class 12
MATHS
Let A={x in R :0lt=xlt=1}dot If f: A->A...

Let `A={x in R :0lt=xlt=1}dot` If `f: A->A` is defined by `f(x)={(x ,, if x in Q) , (1-x ,, if x!in Q):}` then prove that `fof(x)=x` for all `x in Adot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx in Q, 1-x ,ifx notin Q then prove that fof(x)=x for all x in Adot

Let f:R rarr R be given by f(x)={"5x ,if x in Q ", "x^ 2 + 6",if x in R-Q then

Let A={x in R :-4lt=xlt=4 and x!=0} and f: A->R be defined by f(x)=(|x|)/x . Write the range of fdot

If f:[0,1]to[0,1] is defined by f(x)={{:(x," if x is rational"),(1-x," if x is irrational"):} , then (fof)(x) is

The function f(x)={{:( 1, x in Q),(0, x notin Q):} , is

If f: R->R be defined as follows: f(x)={1,\ if\ x in Q-1,\ if\ x !in Q Find: range of fdot

If f(x) = (a-x^n)^(1/n), a > 0 and n in N , then prove that f(f(x)) = x for all x.

If f\ : R-> R be defined by f(x)=(3-x^3)^(1//3)\ , then find fof(x)

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

If f\ : R-: R be defined by f(x)=(3-x^3)^(1//3)\ , then find fof(x)

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f: Rvec (-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x...

    Text Solution

    |

  2. Let f: ZrarrZ be defined by f(n)=3n for all n in Z and g: ZrarrZ be d...

    Text Solution

    |

  3. Let A={x in R :0lt=xlt=1}dot If f: A->A is defined by f(x)={(x ,, if ...

    Text Solution

    |

  4. Let A=[-1,1]dot Then, discuss whether the following functions from A t...

    Text Solution

    |

  5. Let R be a relation on the set A of ordered pairs of positive intege...

    Text Solution

    |

  6. Let A be a finite set. If f: AvecA is an onto function, show that f is...

    Text Solution

    |

  7. Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is ...

    Text Solution

    |

  8. Show that the function f: Rvec R given by f(x)=x^3+x is a bijection.

    Text Solution

    |

  9. Let f: Nuu{0}->Nuu{0} be defined by f={(n+1 ,, ifn \ i s \ e v e n),(n...

    Text Solution

    |

  10. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

    Text Solution

    |

  11. Let A={1,2} . Find all one-to-one function from A to A.

    Text Solution

    |

  12. Let f: Rveca n dg: RvecR be defined by f(x)=x+1a n dg(x)=x-1. Show tha...

    Text Solution

    |

  13. Verify assoiativity for the following three mappings : f: N->Z0 (t...

    Text Solution

    |

  14. If the set A contains 5 elements and the set B contains 6 elements, th...

    Text Solution

    |

  15. If the set A contains 7 elements and the set B contains 10 elements, ...

    Text Solution

    |

  16. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

    Text Solution

    |

  17. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  18. Let A={1,2,3}dot Write all one-one from A to itself.

    Text Solution

    |

  19. If f: RvecR be the function defined by f(x)=4x^3+7, show that f is a b...

    Text Solution

    |

  20. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

    Text Solution

    |