College Algebra, Chapter 3, 3.6, Section 3.6, Problem 4

Find the expression of the function algebraically of the statement.
If the rule of the function $f$ is "add one" and the rule of the function $g$ is "multiply by 2", then the rule of $f \circ g$ is "multiply by 2 then add one" and the rule of $g \circ f$ is "add one then multiply the result by 2."

$
\begin{equation}
\begin{aligned}
f(x) &= \underline{\phantom{x}x + 1\phantom{x}} &&& g(x) &= \underline{\phantom{x}2x\phantom{x}}\\
\\
f \circ g (x) &= \underline{\phantom{x}2x + 1\phantom{x}} &&& g \circ f (x) &= \underline{\phantom{x}2 (x+1)\phantom{x}}
\end{aligned}
\end{equation}
$