Home
Class 12
MATHS
Let S be the set of non-negative integer...

Let S be the set of non-negative integers. A function `f: S to S` is such that `f(f(x) - x) = f(x) - x AA x in S` and the function g(x) = f(x) - x is one-one. Then prove that f(x) = x.

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-I|47 Videos

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-II|20 Videos

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-I|24 Videos

  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

Similar Questions

Explore conceptually related problems

Let f be a function from a set X to X, such that (f(f(x)) = x, for all x in X , then

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Prove that f(x) given by f(x+y)=f(x)+f(y)AA x in R is an odd function.

If f(x) is a real valued function such that f(x + 6) - f(x + 3) + f(x) = 0, AA x in R , then period of f(x) is

Let f ,g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is

" Let "f:A rarr R" be a function such that "f(-x)=f(x),AA X in A" then "f" is "

Let A={xinR:x" is not a positive integer "} define a function f:AtoR" such that "f(x)=(2x)/(x-1) . Then f is

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.

FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-II
  1. Let f : {x,y, z} to {a, b, c} be a one-one function. If it is known th...

    Text Solution

    |

  2. Let S be the set of non-negative integers. A function f: S to S is suc...

    Text Solution

    |

  3. Find the range of f(x), where f(x)=cos(sin(In(x^2+e)/(x^2+1)))+sin(cos...

    Text Solution

    |

  4. Consider two functions, f(x) and g(x) defined as under: f(x)={1+x^3,x ...

    Text Solution

    |

  5. If the functions f and g defined from the set of real number R to R su...

    Text Solution

    |

  6. If the functions f, g and h are defined from the set of real numbers R...

    Text Solution

    |

  7. Let f(x)=2cos^2x+sqrt(3)*sin2x+1. Then, its domain and range, so that ...

    Text Solution

    |

  8. Let f: XtoY be a function defined by f(x) =asin(x+(pi)/4) + bcosx + c....

    Text Solution

    |

  9. Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

    Text Solution

    |

  10. Solve the following equations x^(2)-3-{x}=0 where [x] denotes the ...

    Text Solution

    |

  11. Consider a real-valued function f(x) satisfying 2f(x y)=(f(x))^y+(f(y)...

    Text Solution

    |

  12. If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all x,y in R and ...

    Text Solution

    |

  13. Let f be a function from be set of positive integers to the set of rea...

    Text Solution

    |

  14. Let f be a function from be set of positive integers to the set of rea...

    Text Solution

    |

  15. If the range of the function f(x)=(x-1)/(p-x^2+1) does not contain any...

    Text Solution

    |

  16. Let f :[1/2,oo)rarr[3/4,oo), where f(x)=x^2-x+1. Find the inverse of f...

    Text Solution

    |

  17. Let f(x) be a function such that : f(x - 1) + f(x + 1) = sqrt3 f(x), f...

    Text Solution

    |