College Algebra, Chapter 3, 3.6, Section 3.6, Problem 52

Given $\displaystyle G(x) = \frac{1}{x+3} $, find functions $f$ and $g$ such that $F = f \circ g$
Since the formula for $G$ says to first add 3 then the result is the divisor of 1, we let
$g(x) = x + 3$ and $\displaystyle f(x) = \frac{1}{x}$

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