How do you find the compositions given $g (x) = 3 x + 2$ $g(x) = 3x + 2$ and $h (x) = 9 x^{2} + 12 x + 9$ $h(x) = 9x^2 + 12x + 9$ ?

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How do you find the compositions given $g (x) = 3 x + 2$ $g(x) = 3x + 2$ and $h (x) = 9 x^{2} + 12 x + 9$ $h(x) = 9x^2 + 12x + 9$ ?

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Answer 1 · 2016-01-04T04:04:29

$g (h (x)) = 27 x^{2} + 36 x + 29$ $g(h(x))=27x^2+36x+29$
$h (g (x)) = 81 x^{2} + 144 x + 69$ $h(g(x))=81x^2+144x+69$

Explanation:

Function compositions are basically plugging one function into another function.

To find $g (h (x))$ $g(h(x))$ , take $h (x)$ $h(x)$ , which is $9 x^{2} + 12 + 9$ $9x^2+12+9$ , and plug it into the $x$ $x$ in $g (x)$ $g(x)$ .

$g (x) = 3 x + 2$ $g(color(blue)(x))=3color(blue)x+2$
$h (x) = 9 x^{2} + 12 x + 9$ $h(x)=9x^2+12x+9$

$g (h (x)) = 3 (9 x^{2} + 12 x + 9) + 2$ $g(color(blue)(h(x)))=3color(blue)((9x^2+12x+9))+2$
$g (h (x)) = 27 x^{2} + 36 x + 27 + 2$ $g(h(x))=27x^2+36x+27+2$
$g (h (x)) = 27 x^{2} + 36 x + 29$ $g(h(x))=27x^2+36x+29$

To find $h (g (x))$ $h(g(x))$ , do the process with the roles switched: $g (x)$ $g(x)$ is plugged into $h (x)$ $h(x)$ .

$h (g (x)) = 9 {(3 x + 2)}^{2} + 12 (3 x + 2) + 9$ $h(g(x))=9(3x+2)^2+12(3x+2)+9$
$h (g (x)) = 9 (9 x^{2} + 12 x + 4) + 36 x + 24 + 9$ $h(g(x))=9(9x^2+12x+4)+36x+24+9$
$h (g (x)) = 81 x^{2} + 108 x + 36 + 36 x + 33$ $h(g(x))=81x^2+108x+36+36x+33$
$h (g (x)) = 81 x^{2} + 144 x + 69$ $h(g(x))=81x^2+144x+69$

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How do you find the compositions given $g (x) = 3 x + 2$ $g(x) = 3x + 2$ and $h (x) = 9 x^{2} + 12 x + 9$ $h(x) = 9x^2 + 12x + 9$ ?

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Explanation:

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How do you find the compositions given g(x) = 3x + 2g(x)=3x+2g(x) = 3x + 2 and h(x) = 9x^2 + 12x + 9h(x)=9x2+12x+9h(x) = 9x^2 + 12x + 9?

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Explanation:

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How do you find the compositions given $g (x) = 3 x + 2$ $g(x) = 3x + 2$ and $h (x) = 9 x^{2} + 12 x + 9$ $h(x) = 9x^2 + 12x + 9$ ?