Home
Class 11
MATHS
Polynomial function f(x) satisfying the...

Polynomial function f(x) satisfying the condition `f(x), f(1/x)=f(x)+f(1/x)`. If f(10)=1001, then f(20) is

A

7001

B

8001

C

8000

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|81 Videos

  • FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

A polynomial f(x0 satisfies the condition f(x).f(1/x)=f(x)+f(1/x) and f(10) = 1001, then the value of f(2) =?

If the function f(x) satisfies the condition f(x + 1/x) = x^2 + 1/x^2,x ne 0 then f(x) is

If f: RR^(+) rarr RR ^(+) is a polynomial function satisfying the functional equation f{f(x)}=6x-f(x) , then f(17) is equal to ___

If f(x) is a polynomial satisfying f(x)f(1//x)=f(x) +f(1//x) and f(3)=28, then f(4) is equal to

If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) and f(4)=65 ,then find f(6)

A real valued function f(x) satisfies the functional equation f(x-y) = f(x) f(y) - f(a-x) f(a+y) , where a is a given constant and f(0)=1 , f(2a-x) =?

A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R then f is

If f: R^+rarrR^+ is a polynomial function satisfying the functional equation f(f(x))=6x-f(x),t h e nf(17) is equal to 17 (b) 51 (c) 34 (d) -34

If f(x) = 1/(1-x) , then f[f{f(x)}] is

A real valued function f (x) satisfied the functional relation f (x-y)=f (x)f(y) -f(a-x) f(a+y) where a is a given constant and f(0) =1. Then f (2a-x) is equal to-

PATHFINDER-FUNCTION-QUESTION BANK
  1. If a, b be two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2 ...

    Text Solution

    |

  2. Period of f(x)=sin, pi/2 x+2cos, pi/3 x-tan, pi/4 x is equal to

    Text Solution

    |

  3. Polynomial function f(x) satisfying the condition f(x), f(1/x)=f(x)+f...

    Text Solution

    |

  4. The function f(x) is defined for all real x. If f(a+b)=f(ab) AA a and...

    Text Solution

    |

  5. If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and ...

    Text Solution

    |

  6. If fog=|sinx| and gof=sin^2 sqrtx then f(x) and f(x) are

    Text Solution

    |

  7. 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

    |

  8. Let f(x)={(-1+sinK1pix, x is rational), (1+cosK2pix, x is irrational...

    Text Solution

    |

  9. Let f(1)=1 and f(n)=2overset(n-1)underset(r=1)sum f( r ). Then overset...

    Text Solution

    |

  10. Given f(x) = In {(1+x)/(1-x)} and g(x)={(3x+x^3)/(1+3x^2)}. Then f(g(x...

    Text Solution

    |

  11. If f: [2,3) rarr [0,1) is defined by f(x)=x-[x], the fractional part o...

    Text Solution

    |

  12. The domain of y=cos^-1((1-2|x|)/3)+log|x-1|x is

    Text Solution

    |

  13. Let f:[-pi/3, 2pi/3] rarr [0,4] be a function defined as f(x)=sqrt3 si...

    Text Solution

    |

  14. Let n be a positive integer with f(n)=1!+2!+3!+….+n! and P(x) and Q(x)...

    Text Solution

    |

  15. A function f:R rarr R is defined by f(x+y)-kxy=f(x)+2y^2, AA xy in R a...

    Text Solution

    |

  16. If f(x)=1+x^2 and [g(x)]=1+x^2-2x^3+x^4, g(2)=2, then

    Text Solution

    |

  17. pi is the FUNDAMENTAL period of

    Text Solution

    |

  18. If the range of the function y=(x-1)/(a-x^2+1) does not contain any va...

    Text Solution

    |

  19. Let f: d rarr R be defined by f(X)=In (In(In(In x))) then

    Text Solution

    |

  20. Let f(x)=max{1+sinx,1,1-cosx}, xin[0,2pi] and g(x)=max{1,|x-1|} x in R...

    Text Solution

    |