Answer
$f(x)=\sqrt x$ and $a=9$
Work Step by Step
*According to definition, the derivative of a function $f$ at a number $a$ is $$f'(a)=\lim\limits_{h\to0}\frac{f(a+h)-f(a)}{h}$$
Here we have
$$\lim\limits_{h\to0}\frac{\sqrt{9+h}-3}{h}$$
$$\lim\limits_{h\to0}\frac{\sqrt{9+h}-\sqrt9}{h}$$
Now we match the formula found above with the formula of the derivative according to definition. We find that $a=9$ and $f(a)=f(9)=\sqrt9$
Therefore, $f(x)=\sqrt{x}$
