BdMO Online Forum

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 $f (1952)$?

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

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

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