Home
Class 12
MATHS
Let A = R-{2} and B = R - {1}. If f : A ...

Let A = R-{2} and B = R - {1}. If f : A `rarr` B is a function defined by f(x)= `(x-1)/(x-2)` then show that f is one-one and onto. Hence, find `f^(-1)`.

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2020

    SHARAM PUBLICATION|Exercise EXERCISE|47 Videos
  • THREE DIMENSIONAL GEOMETRY

    SHARAM PUBLICATION|Exercise EXAMPLE|96 Videos

Similar Questions

Explore conceptually related problems

If f:R to R is the function defined by f(x)=4x^(3) +7 , then show that f is a bijection.

Show that the fuction f in A=R-{2/3} definde as f(x)=(4x+3)/(6x-4) is one-one and on to. Hence find f^(-1) .

Show that the function f:R to R defined by f(x)=(x)/(x^(2)+1) is neither one-one nor onto.

If A = R -{3} and B = R -{1}. Consider the function f:A to B defined by f(x)=(x-2)/(x-3) , for all x in A . Then, show that f is bijective. Find f^(-1)(x) .

If f: R rarr R is defined by f(x) = 3x + 2 define f (f (x))

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

Show that the fuction f:RrarrR defined by f (x)=sin x is neither one-one nor onto.

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

Let A=R-{3/5} Br f:ArarrA defined as f(x)=(3x+2)/(5x-3) . Br show that is invertible, hence find f^-1.

Let f: R rarr R be defined by f(x) = 2x - 3 and g: R rarr R be defined by g(x) = (x+3)/(2) , show that fogʻ= I_(R)

SHARAM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE
  1. Check whether the relation R defined on the set A = {1,2,3,4,5,6} as R...

    Text Solution

    |

  2. If the function'f : R rarrR is given by f(x) = x^(2) +2 and g:R rarr R...

    Text Solution

    |

  3. Let A = R-{2} and B = R - {1}. If f : A rarr B is a function defined b...

    Text Solution

    |

  4. Show that the fuction f in A=R-{2/3} definde as f(x)=(4x+3)/(6x-4) is ...

    Text Solution

    |

  5. Show that f : N to N, given by f(x)= {(x+1", if x is odd"),(x-1", if...

    Text Solution

    |

  6. Let f : W rarr W be defined as f (x) = x -1 if x is odd and f(x) = x +...

    Text Solution

    |

  7. If f:R to R is defined as f(x)=10x +7. Find the function g:R to R, suc...

    Text Solution

    |

  8. If f:R to R is the function defined by f(x)=4x^(3) +7, then show that ...

    Text Solution

    |

  9. If the function f:RrarrR is given by f (x)=(x)^2+3x+1 and g:RrarrR is ...

    Text Solution

    |

  10. If S is the set of all rational numbers except 1 and * be defined on S...

    Text Solution

    |

  11. If S is the set of all rational numbers except 1 and * be defined on S...

    Text Solution

    |

  12. Construct the multiplication table times7 on the set {1, 2, 3, 4, 5, 6...

    Text Solution

    |

  13. Consider the binary operation **:R xxR to R and o:R xx R to R defined ...

    Text Solution

    |

  14. Consider the binary operation **on the set {1, 2, 3 , 4, 5} defined by...

    Text Solution

    |

  15. If ** is a binary operation on set Q of rational numbers such tht a**b...

    Text Solution

    |

  16. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

    Text Solution

    |

  17. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

    Text Solution

    |

  18. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |