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`
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SSP|55 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise JEE MAIN|15 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 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

RESONANCE ENGLISH-RELATION, FUNCTION & ITF-HLP_TYPE
  1. If f(x)=(sin^2 x+4sinx+5)/(2sin^2x+8sinx+8) then range of f(x) is

    Text Solution

    |

  2. Find range of the function f(x)=log(2)[3x-[x+[x+[x]]]] (where [.] is...

    Text Solution

    |

  3. If f(x)=1/(x^(2)+1) and g(x)=sinpix+8{x/2} where {.} denotes fractiona...

    Text Solution

    |

  4. The period of sin(pi/4)x+cos(pi/2)x+cos(pi/3)x is

    Text Solution

    |

  5. Consider the function g(x) defined as g(x) (x^(2011-1)-1)=(x+1)(x^2+1)...

    Text Solution

    |

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

    Text Solution

    |

  7. Find the integral solutions to the equation [x][y]=x+y. Show that all ...

    Text Solution

    |

  8. Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if...

    Text Solution

    |

  9. Let g: Rvec(0,pi/3) be defined by g(x)=cos^(-1)((x^2-k)/(1+x^2)) . The...

    Text Solution

    |

  10. Let 0ltalpha,beta,gammalt(pi)/2 are the solutions of the equations cos...

    Text Solution

    |

  11. Let f(x)=(log)2(log)3(log)4(log)5(sin x+a^2)dot Find the set of values...

    Text Solution

    |

  12. Express cot(cosec^(-1)x) as an algebraic function of x.

    Text Solution

    |

  13. Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1...

    Text Solution

    |

  14. Find the inverse of f(x)={(x ,, x<1),(x^2 ,, 1lt=xlt=4),(8sqrt(x) ,, x...

    Text Solution

    |

  15. sin^(-1)((x^(2))/(4)+(y^(2))/(9))+cos^(-1)((x)/(2sqrt(2))+(y)/(3sqrt(2...

    Text Solution

    |

  16. If alpha=2 tan^-1((1+x)/(1-x)) and B= sin^-1((1-x^2)/(1+x^2)) for ...

    Text Solution

    |

  17. Solve {cos^(-1)x}+[tan^(-1)x]=0 for real values of x. Where {.} and [....

    Text Solution

    |

  18. Find the set of all real values of x satisfying the inequality sec^(-1...

    Text Solution

    |

  19. Find the solution of sin^(-1)(x/(1+x))-"sin"^(-1)(x-1)/(x+1)="sin"^(-1...

    Text Solution

    |

  20. Find the number of positive integral solution of the equation Tan^(-1...

    Text Solution

    |