## Rangpur Secondary 2011/7

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Moon
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Contact:

### Rangpur Secondary 2011/7

Problem 7:
Let \$f(x)\$ be a function with the two properties
(a) for any two real numbers \$x\$ and \$y\$, \$f (x+ y)= x+ f (y)\$ and
(b) \$f (0)= 19\$
What is the value of \$f (1952)\$?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

learn how to write equations, and don't forget to read Forum Guide and Rules.

Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm

### Re: Rangpur Secondary 2011/7

\$f(-1952+1952)=-1952+f(1952)\$
or,\$f(0)=-1952+f(1952)\$
so\$f(1952)=1971\$
the ans is 1 of my fav nums
বড় ভালবাসি তোমায়,মা

*Mahi*
Posts: 1175
Joined: Wed Dec 29, 2010 12:46 pm
Location: 23.786228,90.354974
Contact:

### Re: Rangpur Secondary 2011/7

Just another way-
\$f(x+0)=x+f(0)\$
So,\$f(x)=x+19\$
Which means \$f(1952)=1952+19=1971\$

Use \$L^AT_EX\$, It makes our work a lot easier!