Home
Class 12
MATHS
f:N to N, where f(x)=x-(-1)^(x), Then f ...

`f:N to N,` 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

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)={(x-1",", x " is even"),(x+1",",x " is odd"):},` which is clearly one-one and onto.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

f: N rarr N, 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

Let f:N rarr N, where f(x)=x+(-1)^(x-1), then the inverse of is.

Let f: N to N be defined by f(x) = x-(1)^(x) AA x in N , Then f is

Let f:N rarr N given by f(x)=x+(-1)^(x+1), then

If f(x) is continuous at x=1 , where f(x)=(x^(n)-1)/(x-1) , for x != 1 , then f(1)=

If f(x)=(a-x^n)^(1/n) then find f(f(x))

If f(x)=x^(n)-a^(n)",then find "f'(1) .

The function f:N rarr N defined by f(x)=x-5[(x)/(5)] where N is a set of natural numbers,then

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. Let R be the relation on the set R of all real numbers defined by a R ...

    Text Solution

    |

  2. The function f: NvecN(N is the set of natural numbers) defined by f(n)...

    Text Solution

    |

  3. f:N to N, where f(x)=x-(-1)^(x), Then f is

    Text Solution

    |

  4. If S be the set of all triangles and f : S -> R^+, f(Delta) = Area of...

    Text Solution

    |

  5. The function f:(-oo,-1)vec(0, e^5) defined by f(x)=e^x^(3-3x+2) is man...

    Text Solution

    |

  6. Let f:N->N be defined by f(x)=x^2+x+1,x in N. Then is f is

    Text Solution

    |

  7. Let X={a1, a2, ,a6}a n dY={b1, b2,b3}dot The number of functions f fro...

    Text Solution

    |

  8. Which of the following functions is an injective (one-one) function in...

    Text Solution

    |

  9. Given the function f(x)=(a^x+a^(-x))/2(w h e r ea >2)dotT h e nf(x+y)+...

    Text Solution

    |

  10. If f(x)=cos (logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

    Text Solution

    |

  11. The domain of the function f(x)=(1)/(sqrt(""^(10)C(x-1)-3xx""^(10)C(x)...

    Text Solution

    |

  12. The domain of the function f(x)=(sin^(-1)(3-x))/("In"(|x|-2)) is

    Text Solution

    |

  13. The domain of f(x)=(log(2)(x+3))/(x^(2)+3x+2) is

    Text Solution

    |

  14. The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the gre...

    Text Solution

    |

  15. The domain of the function f(x)=log(3+x)(x^(2)-1) is

    Text Solution

    |

  16. Domain of the function, f(x)=[log10 ((5x-x^2)/4)]^(1/2) is

    Text Solution

    |

  17. The domain of f(x)=log|logx| is

    Text Solution

    |

  18. If x^3f(x)=sqrt(1+cos2x)+|f(x)|, (-3pi)/4ltxlt(-pi) /2 and f(x)=(alpha...

    Text Solution

    |

  19. The function f(x)=(sec^(-1)x)/(sqrt(x)-[x]), where [x] denotes the gre...

    Text Solution

    |

  20. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |