College Algebra, Chapter 3, 3.6, Section 3.6, Problem 58

Given $\displaystyle G(x) = \frac{2}{(3+\sqrt{x})^2}$, find functions $f,g$ and $h$ such that $F = f \circ g \circ h$

Since the formula for $G$ says to first take the square root and add 3. Then take the square and lastly, the result is the divisor of 2.
$h(x) = 3+\sqrt{x}, \quad g(x) = x^2, \quad$ and $\displaystyle f(x) = \frac{1}{x}$

$\begin{equation} \begin{aligned} \text{Then } (f\circ g\circ h)(x) &= f(g(h(x))) && \text{Definition of } f \circ g \circ h\\ \\ (f\circ g\circ h)(x) &= f(g(3+\sqrt{x})) && \text{Definition of } h\\ \\ (f\circ g\circ h)(x) &= f\left((3+\sqrt{x})^2 \right) && \text{Definition of } g\\ \\ (f\circ g\circ h)(x) &= \frac{1}{(3 + \sqrt{x})^2} && \text{Definition of } f\\ \\ (f\circ g\circ h)(x) &= G(x) \end{aligned} \end{equation}$