Answer
$f(x) = 2^x $
$a = 3$
Work Step by Step
The form of the equation given resembles the form
$\lim\limits_{h \to 0}$ $\frac{f(h+a) - f(a)}{h}$
In this case, we have $f(a+h)$ = $2^{3+h}$. So, $a = 4$ since it is being added to $h$. This is further supported by the $f(a)$ term, which is $8$, or $2^3$. Thus, $f(x) = 2^x $ and $a = 3$
