Saved Bookmarks
| 1. |
f:RrarrR is a function satisfying `f(x+5)gef(x)+5 and f(x+1)lef(x)+1`. Given `f(1)=1` and `g(x)=f(x)+1-x, g(2009)` is equal toA. `2009`B. `2008`C. `1`D. None of these |
|
Answer» Correct Answer - C `f(x+5)gef(x)+5 ….(i)` and `f(x+1)lef(x)+1 …(ii)` or `f(x)ge f(x+1)-1….(iii)` `implies f(x+5)gef(x)+5gef(x+1)-1+5` or `f(x+5)ge f(x+1)+4…..(iv)` `impliesf(x+5)ge f(x+4)+1` and `therefore (x+1)ge f(x)+1….(v)` `("replacing" x by x-4)` from (ii) and (v) `implies f(x+1)=f(x)+1....(vi)` `therefore f(1)=1` from (vi), f(2), f(3)=3 etc. f(2009) =2009 `therefore g(2009)=f(2009)+1-2009=1` |
|