Home
Class 12
MATHS
Examine whether the following function a...

Examine whether the following function are even or odd or neither even nor odd, where [ ] denotes greatest integer function.
`f(x)={(x|x|,xle-1),([1+x]+[1-x],-1ltxlt1),(-x|x|,xge1):}`

Text Solution

Verified by Experts

The correct Answer is:
even
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise MATCH THE COLUMN|5 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SCQ_TYPE|97 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SSP|55 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

Examine whether the following function are even or odd or neither even nor odd, where [ ] denotes greatest integer function. f(x)=(sec x+x^(2)-9)/(x sin x)

Examine whether the following function are even or odd or neither even nor odd, where [ ] denotes greatest integer function. f(x)=((1+2^(x))^(7))/(2^(x))

Examine whether the following function are even or odd or neither even nor odd, where [ ] denotes greatest integer function. f(x)=sqrt(1+x+x^(2))-sqrt(1-x+x^(2))

Determine whether the following functions are even or odd or neither even nor odd: x+x^(2)

Determine whether the following functions are even or odd or neither even nor odd: sin(x^(2)+1)

Determine whether the following functions are even or odd or neither even nor odd: f(x)=sinx+cosx

Determine whether the following functions are even or odd or neither even nor odd: f(x)=(x^(2)-1)|x|

Determine whether function, f(x)=(-1)^([x]) is even, odd or neither of two (where [*] denotes the greatest integer function).

Find out whether the given function is even,odd or neither f(x)={x|x|x =1,[.] denotes the greatest integer function.

Determine whether the following function are even/odd/neither even nor odd? f(x)=xlog(x+sqrt(x^(2)+1))

RESONANCE-RELATION, FUNCTION & ITF-SUBJECTIVE_TYPE
  1. Examine whether the following function are even or odd or neither even...

    Text Solution

    |

  2. Examine whether the following function are even or odd or neither even...

    Text Solution

    |

  3. Examine whether the following function are even or odd or neither even...

    Text Solution

    |

  4. Which of the following function are not periodic (where [.] denotes gr...

    Text Solution

    |

  5. Which of the following function are not periodic (where [.] denotes gr...

    Text Solution

    |

  6. Which of the following function are not periodic (where [.] denotes gr...

    Text Solution

    |

  7. Find the fundamental period of the following function: f(x)=2+3cos(x...

    Text Solution

    |

  8. Find the fundamental period of the following function: f(x)=sin 3x+c...

    Text Solution

    |

  9. Find the fundamental period of the following function: f(x)="sin" (p...

    Text Solution

    |

  10. Find the fundamental period of the following function: f(x)="cos"3/5...

    Text Solution

    |

  11. Find the fundamental period of the following function: f(x)=1/(1-cos...

    Text Solution

    |

  12. Find the fundamental period of the following function: f(x)=(sin12x)...

    Text Solution

    |

  13. Find the fundamental period of the following function: f(x)=sec^(3)x...

    Text Solution

    |

  14. Let f : D -> R, where D is the domain off. Find the inverse of f, if ...

    Text Solution

    |

  15. Let f:DtoR, where D is the domain of f. Find the inverse of f if it ex...

    Text Solution

    |

  16. Let f:DtoR, where D is the domain of f. Find the inverse of f if it ex...

    Text Solution

    |

  17. Let f:DtoR, where D is the domain of f. Find the inverse of f if it ex...

    Text Solution

    |

  18. R rarr R be defined by f(x)=((e^(2x)-e^(-2x)))/2. is f(x) invertible. ...

    Text Solution

    |

  19. (a) If f(x)=-x|x|, then find f^(-1)(x) and hence find the number of so...

    Text Solution

    |

  20. If g is inverse of f(x) = x^3 + x + cosx, then find the value of g'(...

    Text Solution

    |