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 $f (1952)$?
Rangpur Secondary 2011/7
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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.
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- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
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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
or,$f(0)=-1952+f(1952)$
so$f(1952)=1971$
the ans is 1 of my fav nums
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Re: Rangpur Secondary 2011/7
Just another way-
$f(x+0)=x+f(0)$
So,$f(x)=x+19$
Which means $f(1952)=1952+19=1971$
$f(x+0)=x+f(0)$
So,$f(x)=x+19$
Which means $f(1952)=1952+19=1971$
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Nur Muhammad Shafiullah | Mahi
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- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: Rangpur Secondary 2011/7
mahi i thik we did the same thing but u just defined the general function
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