Home
Class 12
MATHS
If a function f: R ->R be such that f...

If a function `f: R ->R` be such that `f(x-f(y)) = f(f(y) )+xf(y)+f(x) -1 AA x , y in R` then `f(2)=`

A

1

B

3

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`f(x-f(y))=f(f(y))+xy(dy)+f(x)-2" (1)"`
Put `x=f(y)=0`
Then `f(0)=f(0)+0+f(0)-1`
`therefore" "f(0)=1`
Putting `f(y)=x`
`therefore" "f(0)=f(x)+x^(2)+f(x)-1`
Hence, `f(x)=1-(x^(2))/(2)`
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

If a function f:R rarr R be such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1AA x,y in R then f(2)=

Determine all functions f:R rarr R such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1quad AA x,y>=0in R

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 a function f:R rarr R be such that f(1)=2 , f'(0) = ln2 and f(x+y)=2^(x)f(y)+4^(y)f(x),AA x,y in R . If f'(2)=k ln2 ,then number of divisors of k ,is

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

Let a function f:R rarr R such that f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x)AA x,y in R . If f'(2)=kln2 ,then the value of k is

If f:R rarr R satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all x,y in R , then (-f(10))/7 is ……… .

Let f:R rarr R be a function such that f(x+y)=f(x)+f(y),AA x,y in R

Let f be a polynominal such that f(x) f(y) + 2 = f(x) + f(y) + f(xy) AA xx, y in R (0) and f(x) is one one AA xx in R with f(0) = 1 and f (1) = 2 The function y = f(x) is given by

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

    |