Home
Class 12
MATHS
If [.] and {.} denote greatest and fract...

If `[.]` and `{.}` denote greatest and fractional part functions respectively and `f(x)={(x((e^([x]+|x|)-2)/([x]+{2x})),x!=0),(-1,x=0):}` then

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If[.] and {.} denote greatest integer and fractional part functions respectively, then the period of f(x) = e^(sin 3pi{x} + tan pi [x]) is

If f(x)=([{x}]tan^(-1)((x^(2)-3x-1)/(x^(2)-3x-5))+3-x^(7))^(1/7) . Where [k] and {k} denotes greatest integer and fractional part functions of k respectively, then the value of f^(-1)(50)-f(50)+f(f(100)) , is

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

If f(x)=[x^(2)]+sqrt({x}^(2)), where [] and {.} denote the greatest integer and fractional part functions respectively,then

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 :

Solve {x+1}-x^(2)+2x>0( where {.} denotes fractional part function)

The range of function f(x)=log_(x)([x]), where [.] and {.} denotes greatest integer and fractional part function respectively

The value of int_(0)^(|x|){x} dx (where [*] and {*} denotes greatest integer and fraction part function respectively) is

RESONANCE DPP-JEE MAINS-All Questions
  1. If ""^(100)C(6)+4." "^(100)C(7)+6." "^(100)C(8)+4." "^(100)C(9)+""^(1...

    Text Solution

    |

  2. If y=1costheta+2cos2theta+3cos3theta+......+99 cos 99theta , the maxim...

    Text Solution

    |

  3. If [.] and {.} denote greatest and fractional part functions respectiv...

    Text Solution

    |

  4. Prove the trigonometric identities: (1-sintheta)/(1+sintheta)=(secthet...

    Text Solution

    |

  5. Let F(x)=1+f(x)+(f(x))^2+(f(x))^3 where f(x) is an increasing differen...

    Text Solution

    |

  6. Consider the inequality max {1-x^2,|x - 1|}<1 then

    Text Solution

    |

  7. The simultaneous equations, y=x+2|x|&amp; y=4+x-|x| have the solution...

    Text Solution

    |

  8. ABC is an isosceles triangle inscribed in a circle of radius rdot If A...

    Text Solution

    |

  9. If f(x)=a x^2+b x+a^2+b^2+c^2-a b-b c-c a ,w h e r ea ,b ,c are disti...

    Text Solution

    |

  10. If Sn=1^2+(1^2+2^2)+(1^2+2^2+3^2)+ upto n terms, then Sn=(n(n+1)^2(n+2...

    Text Solution

    |

  11. Tangent lines are drawn at the points P and Q where f''(x) vanishes f...

    Text Solution

    |

  12. If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a)(c^2)/(sq...

    Text Solution

    |

  13. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int(0...

    Text Solution

    |

  14. Given that n arithmetic means are inserted between two sets of numbers...

    Text Solution

    |

  15. The greatest value of the function f(x)=(sin2x)/(sin(x+pi/4)) on the i...

    Text Solution

    |

  16. If a,b,and c are three terms of an A.P such that a != b then (b-c)/...

    Text Solution

    |

  17. Least value of |z-2|+|z-4i| is

    Text Solution

    |

  18. Number of solutions of the equation, [y+[y]]=2cosx is: (where y=1//3)[...

    Text Solution

    |

  19. Tangent is drawn at the point (xi ,yi) on the curve y=f(x), which ...

    Text Solution

    |

  20. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...

    Text Solution

    |