Consider the functions f left parenthesis x right parenthesis equals $8$ x minus $6$ and g left parenthesis x right parenthesis equals one eighth left parenthesis x plus $6$ right parenthesis $.$

$($a$)$ Find$$ f$($g$($x$)).$

$($b$)$ Find$$ g$($f$($x$)).$

$($c$)$ Determine whether the functions f and g are inverses of each other.