Chapter 1.5, Problem 70E

(a)

To determine

To find: The value of $\left(fog\right)\left(1\right)$ with the help of graphs of $f$ and $g$ .

Answer to Problem 70E

The value of $\left(fog\right)\left(1\right)$ is equal to $2$ .

Explanation of Solution

Given information:

The graphs of $f$ and $g$ are given below:

  

Calculation:

Simplify the composition function.

  $\left(fog\right)\left(1\right)=f\left(g\left(1\right)\right)$

As observed from the graph of $y=g\left(x\right)$ , the value of $g\left(x\right)$ at $x=1$ is equal to $3$ .

Substitute $3$ for $g\left(1\right)$ in the composition.

  $f\left(g\left(1\right)\right)=f\left(3\right)$

As observed from the graph of $y=f\left(x\right)$ , the value of $f\left(x\right)$ at $x=3$ is equal to $2$ .

Substitute $2$ for $f\left(3\right)$ in the composition.

  $\begin{array}{c}\left(fog\right)\left(1\right)=f\left(g\left(1\right)\right)\\ =f\left(3\right)\\ =2\end{array}$

Therefore, the value of $\left(fog\right)\left(1\right)$ is equal to $2$ .

(b)

To determine

To find: The value of $\left(gof\right)\left(3\right)$ with the help of graphs of $f$ and $g$ .

Answer to Problem 70E

The value of $\left(gof\right)\left(3\right)$ is equal to $2$ .

Explanation of Solution

Given information:

The graphs of $f$ and $g$ are given below:

  

Calculation:

Simplify the composition function.

  $\left(gof\right)\left(3\right)=g\left(f\left(3\right)\right)$

As observed from the graph of $y=f\left(x\right)$ , the value of $f\left(x\right)$ at $x=3$ is equal to $2$ .

Substitute $2$ for $f\left(3\right)$ in the composition.

  $\begin{array}{c}\left(gof\right)\left(3\right)=g\left(f\left(3\right)\right)\\ =g\left(2\right)\end{array}$

As observed from the graph of $y=g\left(x\right)$ , the value of $g\left(x\right)$ at $x=2$ is equal to $2$ .

Substitute $2$ for $g\left(2\right)$ in the composition.

  $\begin{array}{c}\left(gof\right)\left(3\right)=g\left(2\right)\\ =2\end{array}$

Therefore, the value of $\left(gof\right)\left(3\right)$ is equal to $2$ .