recursive language and computable function
The question is about the relation between a computable function $f$ and its graph (here denoted by $L_f$).
Since the function is total, the function is computable if and only if its graph is recursive (in case $f$ is a partial computable function, $f$ is computable if and only if its graph is r.e.).

So, your guess is right, and the correct answer is A. 
To compute $f$ from the characteristic function of the graph, you need to use a generate and test technique, progressively trying all possible outputs y for a given input x (using the characteristic function as tester), until you find the correct pair x#y. Since such a pair must exist, your algorithm is terminating.