Chapter 1.8, Problem 45E

(a)

To determine

To find: The evaluated form of the graph with the help of the given graph.

Answer to Problem 45E

The evaluated value is $0$ .

Explanation of Solution

Given:

The given graph is shown in Figure 1

  

Figure 1

The given equation is $\left(f\circ g\right)\left(2\right)$ .

Calculation:

From the above graph the values of the functions are,

  $\begin{array}{l}f\left(2\right)=0\\ g\left(2\right)=2\end{array}$

Consider the given equation is,

  $\left(f\circ g\right)\left(2\right)=f\left(g\left(2\right)\right)$

Then,

  $\begin{array}{c}\left(f\circ g\right)\left(2\right)=f\left(g\left(2\right)\right)\\ =f\left(2\right)\\ =0\end{array}$

(b)

To determine

To find: The evaluated form of the graph with the help of the given graph.

Answer to Problem 45E

The evaluated value is $4$ .

Explanation of Solution

Given:

The given graph is shown in Figure 2

  

Figure 2

The given equation is $g\circ f\left(2\right)$ .

Calculation:

From the above graph the values of the functions are,

  $\begin{array}{l}f\left(2\right)=0\\ g\left(2\right)=2\\ g\left(0\right)=4\end{array}$

Consider the given equation is,

  $\begin{array}{c}g\circ f\left(2\right)=g\left(f\left(2\right)\right)\\ =g\left(0\right)\\ =4\end{array}$