Home
Class 11
MATHS
If f: Z to Z be given by f(x)=x^(2)+ax+b...

If `f: Z to Z` be given by `f(x)=x^(2)+ax+b`, Then,

A

`a in Z and b in Q-Z`

B

`a,b, in Z`

C

`b in Z and a in Q-Z`

D

`a,b in Q-Z`

Text Solution

Verified by Experts

The correct Answer is:
B
Since `f: Z to Z`. Therefore,
f(x) assumes integral values for all `x in Z`.
`Rightarrow f(0)` and (1) are integers
`Rightarrow` b and a+b+1 are integers
`Rightarrow` b and a integers i.e. ` b in Z`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|49 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^(2)-ax , then f(a)=

Let a,b,c be rational numbers and f:Z->Z be a function given by f(x)=a x^2+b x+c. Then, a+b is

Classify f: Z->Z given by f(x)=x^2 as injection, surjection or bijection.

Let f: Z->Z be given by f(x)={x/2,\ if\ x\ i s\ e v e n,0,\ if\ x\ i s\ od d . Then, f is (a) onto but not one-one (b) one-one but not onto (c) one-one and onto (d) neither one-one nor onto

If f:R to R is given by f(x)=x^(3)+(a+2)x^(2)+3ax+5a if f(x) is one-one function, then a belong to

Classify f: Z->Z given by f(x)=x^3 as injection, surjection or bijection.

Let f = {(1,1), (2, 3), (0, 1), (1, 3)} be a function from Z to Z defined by f(x) = a x + b , for some integers a, b. Determine a, b .

Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in Z .

Check the injectivity and surjectivity of the following functions: (i) f : N ->N given by f(x)=x^2 (ii) f : Z-> Z given by f(x)=x^2 (iii) f : R ->R given by f(x)=x^2 (iv) f : N-> N given by f(x)=x^3 (v) f : Z → Z given by f(x) = x^3

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Chapter Test
  1. If f: Z to Z be given by f(x)=x^(2)+ax+b, Then,

    Text Solution

    |

  2. The number of bijective functions from set A to itself when A contains...

    Text Solution

    |

  3. If f(x)=|sin x| then domain of f for the existence of inverse of

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is - (a)f is one-...

    Text Solution

    |

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

    Text Solution

    |

  8. Find the inverse of the function: f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x))+2

    Text Solution

    |

  9. Find the inverse of the function :y=(1 0^x-1 0^(-x))/(1 0^x+1 0^(-x))+...

    Text Solution

    |

  10. Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals

    Text Solution

    |

  11. Let f : R rarr R, g : R rarr R be two functions given by f(x) = 2x - 3...

    Text Solution

    |

  12. If g(x)=1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) is equal to

    Text Solution

    |

  13. If f(x)=(1-x)/(1+x), x ne 0, -1 and alpha=f(f(x))+f(f((1)/(x))), then

    Text Solution

    |

  14. Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...

    Text Solution

    |

  15. If f:(-oo,2]to (-oo,4] where f(x), then f ^(-1) (x) is given by :

    Text Solution

    |

  16. Find the inverse of the function, (assuming onto). " " ...

    Text Solution

    |

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

    Text Solution

    |

  18. If f(x)=log((1+x)/(1-x))a n dt h e nf((2x)/(1+x^2)) is equal to {f(x)...

    Text Solution

    |

  19. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to 1/2{f(2x)+f(2y...

    Text Solution

    |

  20. The function f:R to R given by f(x)=x^(2)+x is

    Text Solution

    |

  21. Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for ...

    Text Solution

    |