Home
Class 12
MATHS
Prove that the function defined as, F(x)...

Prove that the function defined as, F(x) = {`e^(-sqrt(|ln{x}|)) - {x}^(sqrt(1/(|ln{x}|)))` where ever it exists otherwise {x}, f(x) is odd as well as even.

A

not a periodic function

B

even function

C

range of `f(x)` contains more than 1 element

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
b
`e^(-sqrt(-Int))=t^(1/(sqrt(-Int))),tepsilon(0,1)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

The function f(x) = sin| log (x + sqrt(x^2 + 1)) | is :

The function f(x) = sec[log(x + sqrt(1+x^2))] is

The function f(x)=log(x+sqrt(x^(2)+1)) is

The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

Range of the function f(x)=(ln x)/(sqrt(x)) is

Range of the function f(x)=log_(e)sqrt(4-x^(2)) is

FIITJEE-TEST PAPERS-MATHEMATICS
  1. Consider a function f(x)="sin"^(-1) (2x)/(1+x)+"cos"^(-1) (1-x^(2))/(1...

    Text Solution

    |

  2. Solution of differential equation f^(')(x)f^(''')(x)=3(f^('')(x))^(2),...

    Text Solution

    |

  3. Prove that the function defined as, F(x) = {e^(-sqrt(|ln{x}|)) - {x}^(...

    Text Solution

    |

  4. sum(m=1)^(oo) sum(n=1)^(oo)(m^(2)n)/(3^(m)(n.3^(m)+m.3^(n)))=p/q (wher...

    Text Solution

    |

  5. If f(x)=sum(r=0)^(20) .^(20)C(r) (In (1+x))^(r),g(x)=sum(r=0)^(20)(-1)...

    Text Solution

    |

  6. Let p(x) be a polynomial of degree 6 with leading coefficient unity an...

    Text Solution

    |

  7. If lim(n->oo)[((2009)^2010)^n+((2010)^2009)^n]^(1/n) is equal to a^b w...

    Text Solution

    |

  8. The value of x, x in (2,oo) where f (x) = sqrt(x sqrt(8x-16))+ sqrt(x-...

    Text Solution

    |

  9. A and B are two square matrices such that A^(2)B=BA and if (AB)^(10)=A...

    Text Solution

    |

  10. Delta I(1)I(2)I(3) is an excentral triangle of an equilateral trian...

    Text Solution

    |

  11. If two points P & Q on the hyperbola ,x^2/a^2-y^2/b^2=1 whose centre i...

    Text Solution

    |

  12. If the equation x^(3)-3x+1=0 has three roos x(1),x(2),x(3) where x(1)l...

    Text Solution

    |

  13. Let S={(x,y),x^(2)+y^(2)-6x-8y+21le0} then "max"{(12x)/7-(5y)/7,(x,y...

    Text Solution

    |

  14. The graph of the derivative f of a continuous function f is shown with...

    Text Solution

    |

  15. If f(x)=int(-2)^(x)(t^(4)-bt^(3)+(b+1)t^(2)-bt+b)dt strictly increases...

    Text Solution

    |

  16. Maximum value of function f(x)=(sin^(-1)(sinx)^(2)-sin^(-1)(sinx) is:

    Text Solution

    |

  17. Consider a parabola x^2-4xy+4y^2-32x+4y+16=0. The focus of the parab...

    Text Solution

    |

  18. Let f(x)=ax^(4)+bx^(2)+3x+7 and f(-4)=2286 and f=(4)=N. The number of ...

    Text Solution

    |

  19. The volume of a right triangular prism ABCA1B1C1 is equal to 3. If the...

    Text Solution

    |

  20. If the equation |z(z+1)^8 =z^8 |z+1| where z in C and z(z+1) != 0 ha...

    Text Solution

    |