A fixed point c {\displaystyle c} of the map g ( x ) {\displaystyle g(x)} must satisfy g ( c ) = c . {\displaystyle g(c)=c.} So, we must solve for c {\displaystyle c} in
Rearranging, we have 1 2 c ( 1 − c ) = c − c , {\displaystyle {\frac {1}{2}}c(1-c)=c-c,} which implies that 1 2 c ( 1 − c ) = 0. {\displaystyle {\frac {1}{2}}c(1-c)=0.} Consequently, the two fixed points for the map g ( x ) {\displaystyle g(x)} are c = 0 , 1. {\displaystyle \color {blue}c=0,1.}
