${\displaystyle {}{\begin{aligned}{\left(g\circ f\right)}(x)&=g(f(x))\\&=(f(x))^{2}-1\\&={\left(x^{3}+x\right)}^{2}-1\\&=x^{6}+2x^{4}+x^{2}-1.\end{aligned}}}$

${\displaystyle {}{\begin{aligned}{\left(h\circ g\right)}(y)&=h(g(y))\\&=3(g(y))+4\\&=3{\left(y^{2}-1\right)}+4\\&=3y^{2}-3+4\\&=3y^{2}+1.\end{aligned}}}$

${\displaystyle {}{\begin{aligned}(h\circ g\circ f)(x)&=h((g\circ f)(x))\\&=h(x^{6}+2x^{4}+x^{2}-1)\\&=3(x^{6}+2x^{4}+x^{2}-1)+4\\&=3x^{6}+6x^{4}+3x^{2}-3+4\\&=3x^{6}+6x^{4}+3x^{2}+1\end{aligned}}}$

und andererseits

${\displaystyle {}{\begin{aligned}(h\circ g\circ f)(x)&=(h\circ g)(f(x))\\&=3(f(x))^{2}+1\\&=3(x^{3}+x)^{2}+1\\&=3(x^{6}+2x^{4}+x^{2})+1\\&=3x^{6}+6x^{4}+3x^{2}+1.\end{aligned}}}$