Home
Class 12
MATHS
If f(x) is a polynomial satisfying f(x)f...

If `f(x)` is a polynomial satisfying `f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ,t h e nf(4)` is equal to 63 (b) 65 (c) 17 (d) none of these

A

63

B

65

C

17

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=x^(n)+1`
` or f(3)=3^(n)+1=28`
`or 3^(n)=27`
` :. n=3`
`or f(4)=4^(3)+1=65`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) and f(4)=65 ,t h e nfin df(6)dot

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

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)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

If f(x)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to

If f(x+1/2)+f(x-1/2)=f(x) for all x in R , then the period of f(x) is 1 (b) 2 (c) 3 (d) 4

Suppose that f is differentiable for all x and that f^(prime)(x)lt=2fora l lxdot If f(1)=2a n df(4)=8,t h e nf(2) has the value equal to 3 (b) 4 (c) 6 (d) 8

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. If f is a function such that f(0)=2,f(1)=3,a n df(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  2. A function f(x) satisfies the functional equation x^2f(x)+f(1-x)=2x-x^...

    Text Solution

    |

  3. If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ...

    Text Solution

    |

  4. If f(2x+y/8,2x-y/8)=x y , then f(m , n)+f(n,m)=0 (a) only when m=n (...

    Text Solution

    |

  5. Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(...

    Text Solution

    |

  6. If f(x+y)=f(x)+f(y)-x y-1AAx , y in Ra n df(1)=1, then the number of ...

    Text Solution

    |

  7. The function f Satisfies the functional equation 3 f (x) +2f ((...

    Text Solution

    |

  8. Let f: RvecR be a continuous and differentiable function such that (f(...

    Text Solution

    |

  9. Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...

    Text Solution

    |

  10. If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) ...

    Text Solution

    |

  11. If f(x+1/2)+f(x-1/2)=f(x) for all x in R , then the period of f(x)...

    Text Solution

    |

  12. If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,then f(2) is equal to

    Text Solution

    |

  13. If f(3x+2)+f(3x+29)=AAx in R , then the period of f(x) is 7 (b) 8 ...

    Text Solution

    |

  14. If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, the...

    Text Solution

    |

  15. If f(x)=m a xi mu m{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,...

    Text Solution

    |

  16. Find the values of a for which the equation ||x-2|+a|=4 can have four ...

    Text Solution

    |

  17. Number of integral values of k for which the equation 4 cos^(-1)(-|x|)...

    Text Solution

    |

  18. If f(x) is a real=valued function defined as f(x)=1N(1-sinx), then the...

    Text Solution

    |

  19. Let f(x)=x+2|x+1|+x-1|dotIf f(x)=k has exactly one real solution, then...

    Text Solution

    |

  20. The number of solutions of 2cosx=|sinx|,0lt=xlt=4pi, is 0 (b) 2 (c)...

    Text Solution

    |