Home
Class 12
MATHS
A certain function f(x) has the property...

A certain function f(x) has the property that `f(3x)=alpha f(x)` for all positive real values of x and `f(x)=1-|x-2|` for `1<=x<=3`, `lim_(x->2)(f(x))^(cosec((pi x)/2))` is

A

`2/pi`

B

`-2/pi`

C

`e ^(2//pi)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|7 Videos

  • LIMIT

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|7 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|5 Videos

  • LOGARITHMS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|19 Videos

Similar Questions

Explore conceptually related problems

If f(x)=2 for all real numbers x, then f(x+2)=

If f:RrarrR is a function satisfying the property f(x+1)+f(x+3)=2" for all" x in R than f is

A function f(x) satisfies the functional equation x^2f(x)+f(1-x)=2x-x^4 for all real x. f(x) must be

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

Let f be a real valued function such that f(x)+3xf(1/x)=2(x+1) for all real x > 0. The value of f(5) is

A quadratic function f(x) satisfies f(x)ge0 for all real x. If f(2)=0 and f(4)=12, then the value of f(6) is :

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of f(x).f(-x) for all x is

A function f(x) is such that f(x+pi/2)=pi/2-|x|AAx . Find f(pi/2) , if it exists.

Let f(x)=(alphax)/(x+1),x!=-1. Then write the value of alpha satisfying f(f(x))=x for all x!=-1.

A polynomial function f(x) satisfies the condition f(x)f(1/x)=f(x)+f(1/x) for all x inR , x!=0 . If f(3)=-26, then f(4)=

VIKAS GUPTA (BLACK BOOK) ENGLISH-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. Let f:R->[-1, 1] be defined as f(x) = cos(sin x), then which of the fo...

    Text Solution

    |

  2. Let f (x) =x + sqrt(x^(2) +2x) and g (x) = sqrt(x^(2) +2x)-x, then:

    Text Solution

    |

  3. Which of the following limits does not exist ?(a) lim(x->oo) cosec^(-1...

    Text Solution

    |

  4. If f(x)=(lim)(nvecoo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) where ...

    Text Solution

    |

  5. Let f:R->R;f(x)={(-1)^n if x=1/(2^(2^n)), n=1,2,3.......... and 0 othe...

    Text Solution

    |

  6. If underset(xrarra)(lim)f(x)=underset(xrarra)(lim)[f(x)] ([.] denotes ...

    Text Solution

    |

  7. Let f(x)=(sin^(-1)(1-{x})xxcos^(-1)(1-{x}))/(sqrt(2{x})xx(1-{x})), whe...

    Text Solution

    |

  8. L=underset(xrarr0)(lim)(sin(sinx)-sinx)/(ax^(5)+bx^(3)+c)=-(1)/(12) ...

    Text Solution

    |

  9. If f (x) = lim ( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of...

    Text Solution

    |

  10. lim(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

    Text Solution

    |

  11. If alpha,beta in (-pi/2,0) such that (sin alpha+sinbeta)+(sinalpha)/(s...

    Text Solution

    |

  12. Let f(x)={|x-2|+a^2-6a+9, x < 2 and 5-2x, x >= 2 If lim(x->2) [f(x)] e...

    Text Solution

    |

  13. Iff(x)={x+1/2, x<0 2x+3/4,x >+0 , then [(lim)(xvec0)f(x)]= (where [.] ...

    Text Solution

    |

  14. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

    Text Solution

    |

  15. A certain function f(x) has the property that f(3x)=alpha f(x) for all...

    Text Solution

    |

  16. If L=underset(xto0)lim(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exist...

    Text Solution

    |

  17. If L=underset(xto0)lim(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exist...

    Text Solution

    |

  18. If L=underset(xto0)lim(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exist...

    Text Solution

    |

  19. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

    Text Solution

    |

  20. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

    Text Solution

    |