Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 50

Evaluate each expression using the given table below.


$
\begin{equation}
\begin{aligned}

\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
f(x) & 3 & 1 & 4 & 2 & 2 & 5 \\
\hline
g(x) & 6 & 3 & 2 & 1 & 2 & 3\\
\hline
\end{array}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
& \text{(a)} f(g(1))\\
& \qquad \text{Referring to the table given} f(g(1)) =f(6) = 5.\\
& \text{(b)} g(f(1))\\
& \qquad \text{Referring to the table given} g(f(1)) = g(3) = 2.\\
& \text{(c)} f(f(1))\\
& \qquad \text{Referring to the table given} f(f(1)) = f(3) = 4.\\
& \text{(d)} g(g(1))\\
& \qquad \text{Referring to the table given} g(g(1)) = g(6) = 3.\\
& \text{(e)} (g \circ f)(3)\\
& \qquad \text{Referring to the table given} (g \circ f)(3) =g(4) = 1.\\
& \text{(f)} (f \circ g)(6)\\
& \qquad \text{Referring to the table given} (f \circ g)(6) = f(3) = 4.
\end{aligned}
\end{equation}
$