Home
Class 12
MATHS
It is given that f (x) is defined on R s...

It is given that f (x) is defined on R satisfying `f (1)=1 and ` for `AA x in R,`
`f (x+5) ge f (x) +5 and f (x+1) le f (x) +1`. If `g (x) =f (x) +1-x,` then `g (2002)`= __________

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|6 Videos

  • AREA UNDER CURVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise AXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

If f: R to R is defined as f(x)=2x+5 and it is invertible , then f^(-1) (x) is

let f(x) be a polynomial satisfying f(x) : f(1/x) = f(x) + f(1/x) for all X in R :- {O} and f(5) =126, then find f(3).

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is

If f:R->R and g:R->R is given by f(x) =|x| and g(x)=[x] for each x in R then {x in R:g(f(x))le f(g(x))}

lf f: R rarr R satisfies, f(x + y) = f(x) + f(y), AA x, y in R and f(1) = 4, then sum_(r=1)^n f(r) is

VIKAS GUPTA (BLACK BOOK) ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  2. L e tf(x)={x e^(a x),xlt=0x+a x^2-x^3,x >0 where a is a positive cons...

    Text Solution

    |

  3. Find sum of all possible values of the real parameter 'b' if the diffe...

    Text Solution

    |

  4. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  5. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  6. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  7. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

  8. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  9. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  10. The numbr of real roots of the equation x ^(2013)+ e ^(2014x) =0 is

    Text Solution

    |

  11. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  12. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  13. The coordinates of a particle moving in a plane are given by x (t) = a...

    Text Solution

    |

  14. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

    Text Solution

    |

  15. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  16. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

    Text Solution

    |

  17. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  18. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |

  19. Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in...

    Text Solution

    |

  20. If p (1) and p(2) are the lengths of the perpendiculars from origin on...

    Text Solution

    |