Exercise 1.3.57

Question

Use the given graphs of $f$ and $g$ to evaluate each expression, or explain why it is undefined.
    \begin{enumerate}[label=(\alph*)]
        \item $f(g(2))$
\item $g(f(0))$
\item $(f \circ g)(0)$
\item $(g \circ f)(6)$
\item $(g \circ g)(-2)$
\item $(f \circ f)(4)$
    \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
\item $$f(g(2))=f(5)=4.$$
\item $$g(f(0))=g(0)=3.$$
\item $$(f \circ g)(0)=f(g(0))=f(3)=0.$$
\item $$(g \circ f)(b)=g(f(6))=g(6).$$
Since $6$ does not lie in the domain of $g$, the above statement is undefined.
\item $$(g \circ g)(-2)=g(g(-2))=g(1)=4.$$
\item $$(f \circ f)(4)=f(f(4))=f(2)=-2.$$
\end{enumerate}

Exercise 1.3.57

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Exercise 1.3.57

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