How do you express the function $h(x)=(x + 3)^6$ in the form f o g?

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Answer 1 · 2015-12-29T08:45:57

This can be done in an infinite amount of ways. However, the easiest way is to use the sixth power to your advantage.

$f@g$ means that $g(x)$ is being plugged INTO $f(x)$ , which means that $f(x)$ will have the sixth power in it.

If $h(x)=(x+3)^6$ , $h(x)=(f@g)(x)$ if

$f(x)=x^6$
$g(x)=x+3$

Work backwards: to find $(f@g)(x)$ , take $g(x)$ and put it inside of $f(x)$ --you get $(f@g)(x)=(x+3)^6=h(x)$ .

Other variations include:

$f(x)=sqrtx$
$g(x)=(x+3)^12$
$(f@g)(x)=(x+3)^6$

$f(x)=x+729$
$g(x)=x^6+18 x^5+135 x^4+540 x^3+1215 x^2+1458 x$
$(f@g)(x)=(x+3)^6$

How do you express the function h(x)=(x + 3)^6h(x)=(x + 3)^6 in the form f o g?