Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 51

Evaluate each expression using the graph given below. If it is undefined, explain why.









$
\begin{equation}
\begin{aligned}
& \text{(a)} f(g(2))\\
& \qquad \text {Referring to the graph given} f(g(2)) =f(5) = 4.\\

& \text{(b)} g(f(0))\\
& \qquad \text {Referring to the graph given} g(f(0)) = g(0) = 3.\\

& \text{(c)} (f \circ g)(0)\\
& \qquad \text {Referring to the graph given} (f \circ g)(0) = f(3) = 0.\\

& \text{(d)} (g \circ f)(6)\\
& \qquad \text {Referring to the graph given} (g \circ f)(6) = \text{undefined because $f(6) = 6$ is not a domain of $g$.}\\

& \text{(e)} (g \circ g)(-2)\\
& \qquad \text {Referring to the graph given} (g \circ g)(-2) = g(1) = 4.\\

& \text{(f)} (f \circ f)(4)\\
& \qquad \text {Referring to the graph given} (f \circ f)(4) = f(2) = -2.

\end{aligned}
\end{equation}
$