Question #55f42

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Answer 1 · 2017-04-09T10:59:13

$f@g(x)=3x^2+4$
$g@f(x)=9x^2-12x+6$

Given:

$g(x)=x^2+2$
$f(x)=3x-2$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$f@g(x)$

Where ever there is an $x$ in $f(x)$ write $x^2+2$

$f(color(red)(x))=3color(red)(x)-2" "->" "3(color(red)(x^2+2))-2$

$" "->" "3x^2+4$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$g@f(x)$

Where ever there is an $x$ in $g(x)$ write $3x-2$

$g(color(red)(x))=color(red)(x)^2+2" "->" "(color(red)(3x-2))^2+2$

$" "->" "9x^2-12x+4+2$

$" "->" "9x^2-12x+6$

Answer 2 · 2017-04-09T11:08:28

$f (g(x)) = 3x^2 +4$ ,
$g (f(x)) = 9x^2-12x+6$

$f(x) = 3x-2 ; g(x) =x^2+2$
$f (g(x)) = f (x^2+2) =3 (x^2+2) -2= 3x^2 +4$

$g (f(x)) = g(3x-2) = (3x-2)^2 +2 = 9x^2 -12 x +4 +2 = 9x^2-12x+6$ [Ans]