Home
Class 12
MATHS
Verify whether the function f : A to B ,...

Verify whether the function `f : A to B` , where A = R - {3} and B = R -{1}, defined by `f(x) = (x -2)/(x -3)` is one-one and onto or not. Give reason.

Text Solution

Verified by Experts

The correct Answer is:
f is both one-one and onto.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise SIX MARKS QUESTIONS WITH ANSWERS|7 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (One mark questions)|5 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TWO MARKS QUESTIONS WITH ANSWERS|15 Videos

  • PUC SUPPLEMENTARY EXAMINATION QUESTION PAPER JUNE 2019

    SUBHASH PUBLICATION|Exercise PART E|4 Videos

  • SUPER MODEL QUESTION PAPER FOR PRACTICE

    SUBHASH PUBLICATION|Exercise PART - E|4 Videos

Similar Questions

Explore conceptually related problems

Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f (x) = (x)/(1 + |x|), x in R is one one and onto function.

Let A = R - {3} and B =R -{1}. Consider the function f : A to B defined by f (x) = ((x -2)/(x -3)). Is f one-one and onto ? Justify your answer.

If A to A where A - R - {2/3} defined by f(x) = (4x + 3)/(6x - 4) is invertible. Prove that f^(-1) = f .

Show that the function f : R to R , defined by f(x) = 1/x is one-one and onto, where R, is the set of all non-zero real numbers.

Prove that the function f: R to R, given by f (x) =2x, is one-one and onto.

If f : R to R is defined by f (x) = 2x + 3 , then f^(-1) x

Verify whether the function f : N to Y defined by f(x) = 4x + 3 , where Y = {y : y = 4x + 3, x in N} is invertible or not. Write the inverse of f(x) if exists.

If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) , where m!=n . Then,

SUBHASH PUBLICATION-RELATIONS AND FUNCTIONS -THREE MARKS QUESTIONS WITH ANSWERS
  1. Verify whether the function f : A to B , where A = R - {3} and B = R -...

    Text Solution

    |

  2. If * is a binary operation defined on A = N xx N by (a , b) ** (c, d) ...

    Text Solution

    |

  3. Show that the relation R in the set of all integers, Z defined by R = ...

    Text Solution

    |

  4. Show that the relation R in the set of all natural number, N defined b...

    Text Solution

    |

  5. Show that the relation R in the set A = {x in Z : 0 le x le 12} given ...

    Text Solution

    |

  6. Let R be relation on the set A = {1,2,3,.....,14} by R = {(x,y):3x - y...

    Text Solution

    |

  7. Relation R on Z defined as R = {(x ,y): x - y "is an integer"}. Show t...

    Text Solution

    |

  8. Show that the relation R in R defined R = {(a, b) : a le b} is reflexi...

    Text Solution

    |

  9. Show that if f : R - {7/5} to R - {3/5} is defined by f(x) = (3x + 4)/...

    Text Solution

    |

  10. Show that if f : A to B and g: B to C are one-one, then gof: A to C is...

    Text Solution

    |

  11. Show that if f: A to B and g: B to C are onto, then gof : A to C is al...

    Text Solution

    |

  12. Consider f: N to N, g : N to N and h: N to R defined as f(x) = 2x, g(y...

    Text Solution

    |

  13. If f: X to Y, g : Y to Z and h: Z to S are functions, then ho(gof) = (...

    Text Solution

    |

  14. Let f: X to Y and g: Y to Z be two invertible functions. Then gof is ...

    Text Solution

    |

  15. If R(1) and R(2) are equivalence relations in a set A, show that R(1) ...

    Text Solution

    |

  16. Prove that the relation R defined on the set of real numbers R as R = ...

    Text Solution

    |