ตอนนี้ผมได้ข้อสรุปแล้วครับ
-All continuous functions $f:\mathbb{R} \rightarrow (0,\infty) $ satisfying
$f(x+y) = f(x)f(y)$ are of the form $f(x)=a^x$
-All continuous functions $f : (0,\infty) \rightarrow \mathbb{R}$ satisfying
$f(xy) = f(x)+f(y)$ are of the form $f(x)=log_{a}x$
-All continuous functions $f : (0,\infty) \rightarrow (0,\infty )$ satisfying
$f(xy)=f(x)f(y)$ are of the form $x^t$
|