Answer
$f\circ g = 1-3x$
Domain: $\{x|\Re\}$
$g\circ f =7-3x$
Domain: $\{x|\Re \}$
c) $f\circ f =x$
Domain: $\{x|\Re \}$
d) $g\circ g = 9x+4$
Domain: $\{x|\Re\}$
Work Step by Step
$f\circ g = f(g(x)) = $
$2-(3x+1)=$
$2-3x-1=$
$1-3x$
Domain: $\{x|\Re\}$
$g\circ f = g(f(x)) =$
$3(2-x)+1=$
$6-3x+1=$
$7-3x$
Domain: $\{x|\Re \}$
c) $f\circ f = f(f(x))=$
$2-(2-x)=$
$2-2+x=$
$x$
Domain: $\{x|\Re \}$
d) $g\circ g = g(g(x))=$
$3(3x+1)+1=$
$9x+3+1=$
$9x+4$
Domain: $\{x|\Re\}$
