Home
Class 12
MATHS
Let, the function f:RRrarrRR be defined ...

Let, the function `f:RRrarrRR` be defined by,
`f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" find"`
range of f

Text Solution

Verified by Experts

The correct Answer is:
`{(1,-1)}`
Promotional Banner

Topper's Solved these Questions

  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Short Answer Type Question|60 Videos
  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|72 Videos
  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Multiple choice question|28 Videos
  • REAL NUMBERS

    CHHAYA PUBLICATION|Exercise Exercise (Long Answer Type Questions)|10 Videos
  • RELATION AND FUNCTIONS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|3 Videos

Similar Questions

Explore conceptually related problems

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" find" pre-image of 1 and (-1)

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" Find" f(2),f(sqrt(2)),f(pi),f(2.23),f(e)

If the function f: RR rarr RR be defined by, f(x)={(x " when "x in QQ ),(1-x " when " x in QQ ):} then prove that , (f o f)=I_(RR) .

Let the function f : R to R be defined by f(x)= 2x + cos x , then f(x)-

Let RR and QQ be the sets of real numbers and rational numbers respectively. If a in QQ and f: RR rarr RR is defined by , f(x)={(x " when" x in QQ ),(a-x" when " x notin QQ ):} then show that , (f o f ) (x) = x , for all x in RR

Let RR and QQ be the set of real numbers and rational numbers respectively and f:RR to RR be defined as follows: f(x)={:{(5",", "when "x in QQ),(-5","," when " x !in QQ):} Find f(3),f(sqrt(3)),f(3.6),f(pi),f(e) and f(3.36),

If the function f be defined by f(x) =(2x +1)/(1-3x) , then f ^(-1) (x) is-

Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). Find range of f

Let the function f: RR rarr RR be defined by, f(x)=x^(3)-6 , for all x in RR . Show that, f is bijective. Also find a formula that defines f ^(-1) (x) .

CHHAYA PUBLICATION-RELATION AND MAPPING -Very short answer type questions
  1. What is the difference between a mapping and a relation? Is every rela...

    Text Solution

    |

  2. Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in...

    Text Solution

    |

  3. Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in...

    Text Solution

    |

  4. Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in...

    Text Solution

    |

  5. Find the domain for which the function f(x)=3x^2-2x and g (x) = 9x - ...

    Text Solution

    |

  6. Let C be the set of complex numbers and the function f:RR to RR,g:C ...

    Text Solution

    |

  7. Functions f and g are defined as follows: f:RR- {2}toRR,"where "f(x)...

    Text Solution

    |

  8. Let f be a subset of ZZ xxZZ such that f={(xy,x-y):x, y in ZZ} Is f a ...

    Text Solution

    |

  9. A={-2,-1,0,1,2},B={5,7,11} and f:AtoB,where f(x)=x^2-x +5,then find th...

    Text Solution

    |

  10. Let A = {-2,-1,0,1,2} and f:A to ZZ be defined by f(x) = 2x+1 for all ...

    Text Solution

    |

  11. Let A = {0,1,2,3,4} and f:A to ZZ be defined by f(x) = x^2 -5x+2, find...

    Text Solution

    |

  12. Let A = {0,1,2,3,4} and f:A to ZZ be defined by f(x) = x^2 -5x+2, find...

    Text Solution

    |

  13. Let A={-2,-1,0,1,3/2 ,2},B={-6,-5,-3,0,3,4} and f:AtoB be defined by f...

    Text Solution

    |

  14. Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). F...

    Text Solution

    |

  15. Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). F...

    Text Solution

    |

  16. Let A={0,1},B={2,6},andf:A to B be given by, f(x) =6-4x and g:A to B b...

    Text Solution

    |

  17. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  18. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  19. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  20. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |