It would be a straight line parallel to X-axis

y=cos(cos.....upto infinite times(x))

hence we get

y = cos(y)

u will get a constant value of y

I hope u got the type of graph

I am not sure you can always put y = cos y. Before you do that you have to prove that the series converges. A similar problem was given some time ago.

Please see http://www.goiit.com/posts/list/differenciation-find-the-limit-46157.htm#228305. Hope it helps