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Part $1$

Suppose

f left parenthesis x right parenthesis equals StartRoot x EndRoot plus $4$f$($x$)=$x$+4$

and

g left parenthesis x right parenthesis equals x squared plus ng$($x$)=$x$2+$n$.$

If

f left parenthesis g left parenthesis $8$ right parenthesis right parenthesis equals $6$f$($g$(8))=6,$

what is the value of$$ g$($n$)?$