Home
Class 12
MATHS
If f(x) is a real-valued function discon...

If f(x) is a real-valued function discontinuous at all integral points lying in [0,n] and if `(f(x))^(2)=1, forall x in [0,n],` then number of functions f(x) are

A

`2^(n+1)`

B

`6 times 3^(n)`

C

`2 times 3^(n-1)`

D

`3^(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos

  • FUNCTIONS

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

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 12|4 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

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

  • GRAPHICAL TRANSFORMATIONS

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

Similar Questions

Explore conceptually related problems

If f(x)=x^(2) is a real function, find the value of f(1).

Function f(x)=x-|x| is discontinuous at x=0

If f(x) is a real valued functions satisfying f(x+y) = f(x) +f(y) -yx -1 for all x, y in R such that f(1)=1 then the number of solutions of f(n) = n,n in N , is

If f(x) is continuous and differerntiable function such that f((1)/(n))=0 for all n in N , then

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

The function f(x) is discontinuous only at x = 0 such that f^(2)(x)=1 AA x in R . The total number of such functions is

If f(x) is a real valued function such that f(x + 6) - f(x + 3) + f(x) = 0, AA x in R , then period of f(x) is

Let f:(-1,1)rarrR be a differentiable function satisfying (f'(x))^4=16(f(x))^2 for all x in (-1,1) , f(0)=0. The number of such functions is

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

Let f(x) be a real valued function not identically zero satisfies the equation,f(x+y^(n))=f(x)+(f(y))^(n) for all real x&y and f'(0) 1) is an odd natural number.Find f(10).

ARIHANT MATHS-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. Let f(x)=x^(2)-2x and g(x)=f(f(x)-1)+f(5-f(x)), then

    Text Solution

    |

  2. If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

    Text Solution

    |

  3. If f(x) is a real-valued function discontinuous at all integral points...

    Text Solution

    |

  4. A function f from integers to integers is defined as f(x)={n+3, n in ...

    Text Solution

    |

  5. If f:R->R and f(x)=sin(pi{x})/(x^4+3x^2+7), where {} is a fractional p...

    Text Solution

    |

  6. Let f:R->R and g:R->R be two one-one and onto functions such that they...

    Text Solution

    |

  7. The domain of the funciton f(x) given by 3^(x) + 3^(f) = "min" (2t^(3...

    Text Solution

    |

  8. Let x be the elements of the set A={1,2,3,4,5,6,8,10,12,15,20,24,30,40...

    Text Solution

    |

  9. If A gt 0, c,d,u.v are non-zero constants and the graph of f(x)=abs(Ax...

    Text Solution

    |

  10. If f(x)=x^(3)+3x^(2)+4x+asinx+bcosx, forall x in R is a one-one fuctio...

    Text Solution

    |

  11. If two roots of the equation (p-1)(x^2 +x +1)^2 -(p+1)(x^4+x^2+1)=0 ar...

    Text Solution

    |

  12. Let f(x)=x^(13)+2x^(12)+3x^(11)+...+13x+14 " and " alpha=cos""(2pi)/15...

    Text Solution

    |

  13. Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...

    Text Solution

    |

  14. The complete set of values of a for which the function f(x)=tan^(-1)(x...

    Text Solution

    |

  15. The domain of the function f(x)=sin^(-1)""(1)/abs(x^(2)-1)+1/sqrt(si...

    Text Solution

    |

  16. The domain of f(x)=(log(sin^(-1)sqrt(x^(2)+x+1)))/(log(x^(2)-x+1)) is

    Text Solution

    |

  17. The domain of f(x)=sqrt(sin^(-1)(3x-4x^(3)))+sqrt(cos^(-1)x) is equal ...

    Text Solution

    |

  18. The domain of the function f(x)=root(6)(4^(x)+8^(2//3(x-2))-52-2^(2(...

    Text Solution

    |

  19. The domain of derivative of the function f(x)=abs(sin^(-1)(2x^(2)-1)...

    Text Solution

    |

  20. The range of a function f(x)=tan^(-1){log(5//4)(5x^(2)-8x+4)} is

    Text Solution

    |