College Algebra, Chapter 3, 3.6, Section 3.6, Problem 50

Given $\displaystyle F(x) = \sqrt{x} +1 $, find functions $f$ and $g$ such that $F = f \circ g$
Since the formula for $F$ says to first take the square root and then add 1, we get...
$g(x) = \sqrt{x}$ and $f(x) = x +1$

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