Home
Class 12
MATHS
Let M be the set of all 2xx2 matrices wi...

Let `M` be the set of all `2xx2` matrices with entries from the set `R` of real numbers. Then the function `f: M->R` defined by `f(A)=|A|` for every `A in M` , is (a) one-one and onto (b) neither one-one nor onto (c) one-one but not onto (d) onto but not one-one

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

The function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and onto (b) many-one and onto (c) one-one and into (d) many-one and into

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

The function f:[0,3]->[1,29] , defined by f(x)=2x^3−15x^2+36x+1 , is (a) one-one and onto (b) onto but not one-one (c) one-one but not onto (d) neither one-one nor onto

The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and onto (b) many one and onto (c) one-one and into (d) many one and into

The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and onto (b) one-one but not onto (c) onto but not one-one (d) neither one-one nor onto

A function f from the set of natural numbers to integers is defined by n when n is odd f(n) =3, when n is even Then f is (b) one-one but not onto a) neither one-one nor onto (c) onto but not one-one (d) one-one and onto both

Let f: R-> R , be defined as f(x) = e^(x^2)+ cos x , then is (a) one-one and onto (b) one-one and into (c) many-one and onto (d) many-one and into

The function f:R rarr R defined by f(x)=6+6^|x| is (a) One-one and onto , (b) Many-one and onto (c) One-one and into , (d) Many-one and into

A function f from the set of natural numbers to integers defined by f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d-n/2,\ w h e n\ n\ i s\ e v e n is (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(...

    Text Solution

    |

  2. Let f: R->R be given by f(x)=[x]^2+[x+1]-3 , where [x] denotes the gre...

    Text Solution

    |

  3. Let M be the set of all 2xx2 matrices with entries from the set R o...

    Text Solution

    |

  4. The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and on...

    Text Solution

    |

  5. The range of the function f(x)=\ ^(7-x)P(x-3) is (a) {1, 2, 3, 4, ...

    Text Solution

    |

  6. A function f from the set of natural numbers to integers is defined by...

    Text Solution

    |

  7. Let f be an injective map. with domain (x, y, z and range (1, 2, 3), s...

    Text Solution

    |

  8. Which of the following function from Z to itself are bijections? f(x)=...

    Text Solution

    |

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

    Text Solution

    |

  10. Let A{x :-1lt=xlt=1}a n df: Avec such that f(x)=x|x|, then f is (a) bi...

    Text Solution

    |

  11. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

    Text Solution

    |

  12. If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one...

    Text Solution

    |

  13. The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=sin^(-...

    Text Solution

    |

  14. Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(...

    Text Solution

    |

  15. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!...

    Text Solution

    |

  16. Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is...

    Text Solution

    |

  17. f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-on...

    Text Solution

    |

  18. The function f: R->R , f(x)=x^2 is (a) injective but not surjective (b...

    Text Solution

    |

  19. A function f from the set of natural numbers to integers defined by...

    Text Solution

    |

  20. Which of the following functions from A={x in R :-1lt=xlt=1} to its...

    Text Solution

    |