Rangpur Secondary 2011/7

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Moon
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Rangpur Secondary 2011/7

Unread post by Moon » Wed Feb 02, 2011 6:49 pm

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 $f (1952)$?
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Tahmid Hasan
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Re: Rangpur Secondary 2011/7

Unread post by Tahmid Hasan » Wed Feb 02, 2011 7:54 pm

$f(-1952+1952)=-1952+f(1952)$
or,$f(0)=-1952+f(1952)$
so$f(1952)=1971$
the ans is 1 of my fav nums :D
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Re: Rangpur Secondary 2011/7

Unread post by *Mahi* » Thu Feb 03, 2011 6:13 pm

Just another way-
$f(x+0)=x+f(0)$
So,$f(x)=x+19$
Which means $f(1952)=1952+19=1971$
:D
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Re: Rangpur Secondary 2011/7

Unread post by Tahmid Hasan » Thu Feb 03, 2011 9:19 pm

mahi i thik we did the same thing but u just defined the general function :D
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