My professor today showed us the tent map equation. He used a few examples for x that were common fractions (1/2, 1/3, etc.). Then, he asked what would happen if the input (T(x)) was a fraction such as 1/square root of 2. He wants us to explain to him what outputs we would at so many run throughs of the equation (sorry not using exact terminology my professor didn't explain anything about this equation). Below is the tent map equation. I am kindly asking for ANY help on figuring out what I need to do to solve this problem. I have been running 1/square root of 2 through the equation (currently at 27 times) and have made no real headway. Thanks in advance!
Tent Map Equation: T(x) = 2x for 0 =< x =< 1/2,
2(1 - x) for 1/2 < x =< 1