Answer
$f(x)=x^4, g(x)=\cos x, h(x)=x^2+1$
$f(x)=\cos^4 x, g(x)=x^2, h(x)=\sqrt{x^2+1}$
Work Step by Step
We are given the function:
$Q(x)=\cos^4 (x^2+1)$
The choice of the three functions $f,g,h$ so that $Q(x)=f(g(h(x)))$ is not unique.
Example 1: $f(x)=x^4$
$g(x)=\cos x$
$h(x)=x^2+1$
$f(g(h(x)))=f(g(x^2+1))=f(\cos(x^2+1))=\cos^4 (x^2+1)$
Example 2: $f(x)=\cos^4 x$
$g(x)=x^2$
$h(x)=\sqrt{x^2+1}$
$f(g(h(x)))=f(g(\sqrt{x^2+1}))=f(x^2+1)=\cos^4 (x^2+1)$
