For fixed $k$, ......
We temporarily fix $n$ in $N$.
Fix $n$ for the moment.
Fix $n$ and let $c$ vary.
The mapping $f$ leaves $\langle$keeps$\rangle$ the origin fixed.
Thus $F$ has $x$ as its unique fixed point.
Go to the list of words starting with: a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
y
z