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)=ln(f(x))+ln(g(x))`. Then for real `x , h(x)` is

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let {x} and [x] denote the fractional and integral parts of a real number x respectively. Solve 4{x}=x+[x] .

Let{x} and [x] denote the fractional and integral parts of a real number x respectively.Solve 4{x}=x+[x]

Find the domain and range of f(x)=log{x},w h e r e{} represents the fractional part function).

Two real valued functions f and g are defined respectively by f(x)=log_e(1-x) and g(x)=[x], find the following functions : (f)/(g)

Two real valued functions f and g are defined respectively by f(x)=log_e(1-x) and g(x)=[x], find the following functions : (g)/(f)

Two real valued functions f and g are defined respectively by f(x)=log_e(1-x) and g(x)=[x], find the following functions : f+g

Two real valued functions f and g are defined respectively by f(x)=log_e(1-x) and g(x)=[x], find the following functions : f-g

Two real valued functions f and g are defined respectively by f(x)=log_e(1-x) and g(x)=[x], find the following functions : fg

Draw the graph of f(x) = [log_(e)x], e^(-2) lt x lt 10 , where [*] represents the greatest integer function.

The function f(x)=(ln(pi+x))/(ln(e+x)) is

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Which of the following functions is not periodic? (a)|sin3x|+sin^2x ...

    Text Solution

    |

  2. Find the number of solutions of sinx=x/(10)

    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. Column I: Function, Column II: Period f(x)="cos"(|sinx|-|cosx|) , p...

    Text Solution

    |

  5. Solve sinx gt - (1)/(2) or find the domain of f(x)=(1)/(sqrt(1+2sin x...

    Text Solution

    |

  6. The domain of the function f(x)=x/(sqrt(sin(lnx)-cos(lnx))),(n in Z) ...

    Text Solution

    |

  7. If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a g...

    Text Solution

    |

  8. Let f: N->Z be a function defined as f(x)=x-1000. Show that f is an in...

    Text Solution

    |

  9. If f is a function such that f(0)=2, f(1)=3 and f(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  10. A real valued function f(x) satisfies the functional equation f(x-y) ...

    Text Solution

    |

  11. Find the domain of f(x)=1/(sqrt(x+|x|))

    Text Solution

    |

  12. If f: R->R is a function satisfying the property f(2x+3)+f(2x+7)=2AAx ...

    Text Solution

    |

  13. Suppose that F(n + 1) =(2F(n) + 1)/2 for n = 1,2,3,,,, and F(1) = 2. T...

    Text Solution

    |

  14. Find the domain of f(x)=1/(sqrt(x-|x|))

    Text Solution

    |

  15. Domain of the function f(x)=1/sqrt(^10C(x-1) -3. ^10Cx contains the po...

    Text Solution

    |

  16. If f(x) is an even function and satisfies the relation x^2dotf(x)-2f(1...

    Text Solution

    |

  17. Solve ||x-1|-5|lt=2

    Text Solution

    |

  18. Determine all functions f : R rarr R satisfying f(x-f(y)) = f(f(y)) + ...

    Text Solution

    |

  19. The domain of f(x)=cos^(-1)((2-|x|)/4)+[ log(3-x)]^-1 is (a)[-2,6] ...

    Text Solution

    |

  20. Find the domain of f(x)=sqrt((1-|x|)/(|x|-2))

    Text Solution

    |