Answer
12.56.. I think
umm you haven't said which part of the circles is shaded but I assumed that it's the gap between the two circles

1/9 as a decimal would be 0.111111
Yes - they have to be similar. Since they are using the same line as the hypotenuse, the ratio of the other two sides are in the same ratio (ie, the slope of the line), the 3 inner angles will be the same. Thus, the triangles will be similar.
We assume that the function is as follows:

Then, we have that:

Thus, if we have that:

Therefore, the value for the function is f^-1(2) = -1/2 or
The answer k is n divided by 6