Let f and g be two simple objective functions, taking in input a bit$-$string of length $4$ and returning a real number to be maximized, defined as follows:

def f$($x$)$: return $1+$ x$[0]+$ x$[1]+$ x$[2]+5*$x$[3]$

def g$($x$)$: return $3*$log$($f$($x$))+88\mathrm{.}8$

Also consider a genetic algorithm, called GA$1,$ which uses the following operators: truncament selection, uniform crossover, single bit$-$flip mutation, and comma replacement. Suppose that GA$1$ is run once for each objective function by initializing the random number generator with the same seed. Let indicate the two executions with GA$1($f$,$seed$)$ and GA$1($g$,$seed$).$ Is there a relationship between the solutions evaluated in the executions GA$1($f$,$seed$)$ and GA$1($g$,$seed$)?$ If so$,$ explain what it is and try to discuss a more general property of GA$1.$ Moreover, what if we change the operators of GA$1?$