Home
Class 12
MATHS
Let f(x)=e^({e^(|x|sgnx)})a n dg(x)=e^([...

Let `f(x)=e^({e^(|x|sgnx)})a n dg(x)=e^([e^(|x|sgnx)]),x in R ,` where { } and [ ] denote the fractional and integral part functions, respectively. Also, `h(x)=log(f(x))+log(g(x))`. Then for real `x , h(x)` is

A

an odd function

B

an even function

C

neither odd nor even function

D

both odd as well as even function

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|22 Videos

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 12|4 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Solve 2[x]=x+{x},w h r e[]a n d{} denote the greatest integer function and the fractional part function, respectively.

Let f(x) = log _({x}) [x] g (x) =log _({x}){x} h (x)= log _({x}) {x} where [], {} denotes the greatest integer function and fractional part function respectively. Domine of h (x) is :

Let f(x) = log _({x}) [x] g (x) =log _({x})-{x} h (x) = log _([x ]) {x} where [], {} denotes the greatest integer function and fractional part function respectively. Domine of h (x) is :

If f(x)=log_(x^(2))(logx) ,then f '(x)at x= e is

If f(x)=log_(x) (log x)," then find "f'(x) at x= e

If f(x)=log_(e)(log_(e)x)/log_(e)x then f'(x) at x = e is

Find the domain of the function f(x)=log_(e)(x-[x]) , where [.] denotes the greatest integer function.

Let f(x) = log _({x}) [x] g (x) =log _({x})-{x} h (x) log _({x}) {x} where [], {} denotes the greatest integer function and fractional part function respectively. For x in (1,5)the f (x) is not defined at how many points :

prove "lim"_(xvecoo)(ln x)/([x])="lim"_(xvecoo)([x])/(ln x) where [.] is G.I.F. & {.} denotes fractional part function

Period of the function f(x)=sin(sin(pix))+e^({3x}) , where {.} denotes the fractional part of x is

ARIHANT MATHS ENGLISH-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. Given f(x)= sqrt(8/(1-x)+8/(1+x)) and g(x) = 4/(f(sinx))+4/(f(cosx)) t...

    Text Solution

    |

  2. Let f be a function satisfying of xdot Then f(x y)=(f(x))/y for all po...

    Text Solution

    |

  3. Let f(x)=e^({e^(|x|sgnx)})a n dg(x)=e^([e^(|x|sgnx)]),x in R , where ...

    Text Solution

    |

  4. Which of the following function is surjective but not injective. (a) ...

    Text Solution

    |

  5. If f(x) = 2 x^3 + 7x - 5 then f^(-1) (4) is :

    Text Solution

    |

  6. The range of the function f(x)=(e^(x)*logx*5^(x^(2)+2)*(x^(2)-7x+10)...

    Text Solution

    |

  7. If x=cos^(-1)(cos 4) " and " y=sin^(-1)(sin3), then which of the follo...

    Text Solution

    |

  8. Let f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R. Co...

    Text Solution

    |

  9. If f(x)=e^(sin(x-[x])cospix), where [x] denotes the greatest integer f...

    Text Solution

    |

  10. Find the range of the function f(x)=cot^(-1)(log)(0. 5)(x^4-2x^2+3)

    Text Solution

    |

  11. Range of f(x)=[1/(log(x^(2)+e))]+1/sqrt(1+x^(2)), where [*] denotes gr...

    Text Solution

    |

  12. The period of the function f(x)=Sin(x +3-[x+3]) where [] denotes the g...

    Text Solution

    |

  13. Which one of the following function best represents the graphs as show...

    Text Solution

    |

  14. The solution set for [x]{x}=1 (where {x} and [x] are respectively, fra...

    Text Solution

    |

  15. The domain of definition of function f(x)=log(sqrt(x^(2)-5x-24)-x-2)...

    Text Solution

    |

  16. If f(x) is a function f:R-> R, we say f(x) has property I. If f(f(x)) ...

    Text Solution

    |

  17. Let f(x)=x/(1+x) and let g(x)=(rx)/(1-x) , Let S be the set off all re...

    Text Solution

    |

  18. Let f be a linear function with properties f(1)lef(2),f(3)gef(4)and ...

    Text Solution

    |

  19. Suppose R is relation whose graph is symmetric to both X-axis and Y-ax...

    Text Solution

    |

  20. The area between the curve 2{y} =[x] +1,0 leq y lt 1, where {.} and [....

    Text Solution

    |