Question

sendo f(x)=3x+1 e g(x)=4x - 3 determine as leis que definem fog gof fof e (fog) o (gof)

Answer 1

1)

$f(g(x)) = 3(g(x)) + 1$
$f(g(x)) = 3(4x-3)+1=12x-8$

2)

$g(f(x))=4(f(x))-3$
$g(f(x))=4(3x+1)-3=12x+1$

3) 

$f(f(x))=3(f(x))+1$
$f(f(x))=3(3x+1)+1=9x+4$

4) Como $f(g(x))$ = 12x-8 e $g(f(x))$ = 12x+1, temos que:

$12(12x+1)-8 = f(g(g(f(x))) = 144x+4$