# Decide whether the composite functions, f@g and g@f, are equal to x. f(x)=x^3+9 g(x)=root(3)(x-9)

Decide whether the composite functions, $f\circ g$ and $g\circ f$, are equal to x.
$f\left(x\right)={x}^{3}+9$
$g\left(x\right)=\sqrt[3]{x-9}$
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To find the composite function we need to plug-in function in place of the variable. Mathematically,
$f\circ g=f\left(g\left(x\right)\right)$
$g\circ f=g\left(f\left(x\right)\right)$
Therefore, the composite functions are,
$f\circ g=f\left(\sqrt[3]{x-9}\right)$
$=\sqrt[3]{x-9}+9$
$=x-9+9$
$=x$
$g\circ f=g\left(f\left(x\right)\right)$
$=\sqrt[3]{\left({x}^{3}+9\right)-9}$
$=\sqrt[3]{{x}^{3}}$
=x
Hence, both composite functions are equal to zero.