Home
Class 12
MATHS
Let f(x) be a polynominal one-one functi...

Let f(x) be a polynominal one-one function such that
`f(x)f(y)+2=f(x)+f(y)+f(xy), forall x,y in R-{0}, f(1) ne 1, f'(1)=3.`
Let `g(x)=x/4(f(x)+3)-int_(0)^(x)f(x)dx,` then

A

g(x)=0 has exactly one root for `x in (0,1)`

B

g(x)=0 has exactly two roots for `x in (0,1)`

C

`g(x) ne 0, x in R-{0}`

D

`g(x)=0, x in R-{0}`

Text Solution

Verified by Experts

The correct Answer is:
D
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

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

Let f be a real function such that f(x-y), f(x)f(y) and f(x+y) are in A.P. for all x,y, inR. If f(0)ne0, 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,

abs(f(x)-f(y))le(x-y)^2 forall x,y in R and f(0)=1 then

If f(x) be a differentiable function,such that f(x)f(y)+2=f(x)+f(y)+f(xy);f'(0)=0,f'(1)=2 then find f(x)

Let f(x) be a function such that f(x)*f(y)=f(x+y),f(0)=1,f(1)=4. If 2g(x)=f(x)*(1-g(x))

let f(x) be the polynomial function. It satisfies the equation 2 +f(x)* f(y) = f(x) + f(y) +f(xy) for all x and y. If f(2) =5 find f|f(2)| .

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1_ =a. Then , f (x) =

ARIHANT MATHS-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. The range of the function f(x)=sqrt(x-1)+2sqrt(3-x) is

    Text Solution

    |

  2. The domain of the function f(x)=cos^(-1)(sec(cos^-1 x))+sin^(-1)(cose...

    Text Solution

    |

  3. Let f(x) be a polynominal one-one function such that f(x)f(y)+2=f(x)...

    Text Solution

    |

  4. Let f(x) be a polynominal with real coefficients such that f(x)=f'(x) ...

    Text Solution

    |

  5. Let A={1,2,3,4,5} and f:A rarr A be an into function such that f(i) ne...

    Text Solution

    |

  6. If functions f:{1,2,…,n} rarr {1995,1996} satisfying f(1)+f(2)+…+f(199...

    Text Solution

    |

  7. The range of y=sin^(3)x-6sin^(2)x+11sinx-6 is

    Text Solution

    |

  8. Let f(x)=x^(2)-2x and g(x)=f(f(x)-1)+f(5-f(x)), then

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |