Fixed-Point & Root Relation

Question

Lets say I have found out the fixed point for a given function.

I'm only given a point that is basically mapped to itself, but how do I find the root of the function and thus any solutions using this fixed point I just found?

Answer 1

A fixed point of $f$ is $x$ such that $x = f(x)$. A zero is $x$ such that $f(x) = 0$. Plotting such means that a zero is where the graph for $f$ cuts the $X$ axis, a fixed point is where it cuts the line $y = x$, i.e., the line bisecting the angle between the $X$ and $Y$ axes. Do a few sketches, you will see that there isn't any necesary relation between both values. They might be the same ($x = 0$), the fixed point might be before or after the zero, there might be several zeros and fixed points, or none whatsoever.