$f(x)$ liên tục trên $[0; + \infty ) \Leftrightarrow f(x)$ liên tục tại 0
$\Leftrightarrow \displaystyle \lim_{x \rightarrow 0^+} f(x) = f(0)$
$\Leftrightarrow \displaystyle \lim_{x \rightarrow 0^+} \dfrac{3- \sqrt{9-x}}{x} = m \\
\Leftrightarrow \displaystyle \lim_{x \rightarrow 0^+} \dfrac{9- (9-x)}{x \left ( 3+ \sqrt{9-x} \right )} = m \\
\Leftrightarrow \displaystyle \lim_{x \rightarrow 0^+} \dfrac{9- 9+x}{x \left ( 3+ \sqrt{9-x} \right )} = m \\
\Leftrightarrow \displaystyle \lim_{x \rightarrow 0^+} \dfrac{x}{x \left ( 3+ \sqrt{9-x} \right )} = m \\
\Leftrightarrow \displaystyle \lim_{x \rightarrow 0^+} \dfrac{1}{ \left ( 3+ \sqrt{9-x} \right )} = m \\
\Leftrightarrow \dfrac{1}{ \left ( 3+ \sqrt{9-0} \right )} = m \\
\Leftrightarrow m = \dfrac{1}{6}$