Artificial Neural Networks:

However imagine now in this example as the inputs to our function were arrays of pixels and there actually taken from photographs of vehicles such that the output of the function is either 1, 2 or 3 when 1 stands for a car and 2 stands for a bus and 3 also stands for a tank.

Hence in this case there the function that takes an array of integers representing pixel data and outputs either 1 or 2 or 3 will be fairly complicated then it's just doing the same kind of thing as the two simpler functions. 

Presumably the functions learned an example as categorise photos of vehicles into a category of car or bus or tank then are so complicated that we say the ANN approach is a black box approach is because of that the function performs well at its job so that we cannot look inside it to gain a knowledge of how it works. However this is a little unfair as maybe there are some projects that have addressed the problem of translating learned neural networks into human readable forms. Moreover,, there in generally ANNs are used in cases when the predictive accuracy is  of greater importance than understanding the learned concept.