Home
Class 12
MATHS
Let f: R->R be given by f(x)=[x]^2+[x+1]...

Let `f: R->R` be given by `f(x)=[x]^2+[x+1]-3` , where `[x]` denotes the greatest integer less than or equal to `x` . Then, `f(x)` is (a) many-one and onto (b) many-one and into (c) one-one and into (d) one-one and onto

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

If the function f: R->R be such that f(x) = x-[x], where [x] denotes the greatest integer less than or equal to x, then f^-1(x) is

f: NrarrN, where f(x)=x-(-1)^x . Then f is: (a)one-one and into (b)many-one and into (c)one-one and onto (d)many-one and 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

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

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

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:(-oo,-1)rarr(0, e^5) defined by f(x)=e^(x^3-3x+2) is (a)many one and onto (b)many one and into (c)one-one and onto (d)one-one and into

Let f:R rarr R , then f(x) = 2 x + |cos x| is: (a).One-one into (b).One-one and onto (c).May-one and into (d).Many-one and onto

Let f : R^+ ->{-1, 0, 1} defined by f(x) = sgn(x-x^4 + x^7-x^8-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into (3) one-one and onto (4) one- one and into

Let f:[0,5] to [-1,5] , where f(x)={x^2-1,0 then f(x) is : (A) one-one and onto (B) one-one and into (C) many one and onto (D) many one and into

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. The function f: A->B defined by f(x)=-x^2+6x-8 is a bijection, if A=(-...

    Text Solution

    |

  2. Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |