Home
Class 12
MATHS
Suppose f is a real function satisfying ...

Suppose `f` is a real function satisfying `f(x+f(x))=4f(x)a n df(1)=4.` Then the value of `f(21)` is `16` `21` `64` `105`

A

16

B

64

C

4

D

44

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x+f(x))=4f(x) and f(1)=4`
Put x = 1, then
`f(1+f(1))=4f(1)`
`rArr" "f(5)=16`
Put x = 5, then
`f(5+f(5))=4f(5)`
`rArr" "f(21)=64`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE|Exercise Question Bank|30 Videos

  • FUNCTIONS

    CENGAGE|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE|Exercise DPP 3.4|19 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE|Exercise Exercise|18 Videos

Similar Questions

Explore conceptually related problems

Suppose f is a real function satisfying f(x+f(x))=4f(x) and f(1)=4. Then the value of f(21) is 162164105

If f is a real valued function such that f(x+y)=f(x)+f(y) and f(1)=5 , then the value of f(100) is

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x), then find the period of f(x)

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x), then find the period of f(x)

Let f be a real valued function satisfying f(x)+f(x+6)=f(x+3)+f(x+9).Then int_x^(x+12)f(t)dt is

f(x) is a real valued function, satisfying f(x+y)+f(x-y)=2f(x).f(y) for all yinR , Then

Find the period of the real-valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6).

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

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

CENGAGE-FUNCTIONS-Single Correct Answer Type
  1. If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be two real functions, then the r...

    Text Solution

    |

  2. If domain of f(x) is [1, 3], then the domain of f(log(2)(x^(2)+3x-2)) ...

    Text Solution

    |

  3. Let f(x)=x/(1+x) and let g(x)=(rx)/(1-x) , Let S be the set off all re...

    Text Solution

    |

  4. Let f(x)=(ax + b )/(cx+d). Then the fof (x)=x, provided that : (a!=0,...

    Text Solution

    |

  5. If f :R ->R , f(x)=x^3 +3,and g:R->R,g(x)=2x + 1, then f^(-1)og^(-1)(2...

    Text Solution

    |

  6. If f(x)=x(x-1) is a function from [1/2,oo)to[-1/4,oo), then {x in r :...

    Text Solution

    |

  7. Let agt1 be a real number and f(x)=log(a)x^(2)" for "xgt 0. If f^(-1) ...

    Text Solution

    |

  8. If the function f(x) ={x+1 if x le 1 , 2x+1 if 1 lt x le 2 and g(x) = ...

    Text Solution

    |

  9. Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integ...

    Text Solution

    |

  10. If f(x) is an invertible function and g(x)=2f(x)+5, then the value of ...

    Text Solution

    |

  11. If f(x)={{:(-x+1",",xle0,),(,,",then the number of solutions"),(-(x-1)...

    Text Solution

    |

  12. Let f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0 and f(0)=0 ...

    Text Solution

    |

  13. If f(x^2-6x+6)+f(x^2-4x+4)=2x AA in x in R then f(-3) + f(9) -5f(1)= ...

    Text Solution

    |

  14. If a function f: R ->R be such that f(x-f(y)) = f(f(y) )+xf(y)+f(x)...

    Text Solution

    |

  15. If f: RvecR is a function satisfying f(x+y)=f(x y) for all x ,y in Ra...

    Text Solution

    |

  16. A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for ...

    Text Solution

    |

  17. Let f be a function defined from F^(+)rarrR^(+). If (f(xy))^(2)=x(f(y)...

    Text Solution

    |

  18. Suppose f is a real function satisfying f(x+f(x))=4f(x)a n df(1)=4. Th...

    Text Solution

    |

  19. The graph of a function y = g (x) is shown in the following figure. I...

    Text Solution

    |

  20. Let f: IvecI be a function (I is set of integers) such that f(0)=1,f(f...

    Text Solution

    |