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

Evaluate each expression using the given table below.


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



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