Chapter 14.6, Problem 2CE

a.

To determine

To find the value of $f\left(4\right).$

Answer to Problem 2CE

The value of $f\left(4\right)$ is $2.$

Explanation of Solution

Given two functions: $f:x\to \sqrt{x}\text{ and }g:x\to x+7.$

Calculation:

Plug the value of $x=4$ in $f\left(x\right)=\sqrt{x}.$

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

Thus, the value of $f\left(4\right)$ is $2.$

b.

To determine

To find the value of $gof\left(4\right).$

Answer to Problem 2CE

The value of $\left(gof\right)\left(4\right)\text{ is }9.$

Explanation of Solution

Given two functions: $f:x\to \sqrt{x}\text{ and }g:x\to x+7.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(4\right)=g\left(f\left(4\right)\right)\\ =\sqrt{4+}+7\\ =2+7\\ =9\end{array}$

Thus, the value of $\left(gof\right)\left(4\right)\text{ is }9.$

c.

To determine

To find the value of $\left(gof\right)\left(x\right).$

Answer to Problem 2CE

The value of $\left(gof\right)\left(x\right)\text{ is }\sqrt{x}+7.$

Explanation of Solution

Given two functions: $f:x\to \sqrt{x}\text{ and }g:x\to x+7.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(x\right)=g\left(f\left(x\right)\right)\\ =g\left(\sqrt{x}\right)\\ =\sqrt{x}+7\end{array}$

Thus, the value of $\left(gof\right)\left(x\right)\text{ is }\sqrt{x}+7.$

d.

To determine

To find the value of $g\left(2\right).$

Answer to Problem 2CE

The value of $g\left(2\right)$ is 9.

Explanation of Solution

Given two functions: $f:x\to \sqrt{x}\text{ and }g:x\to x+7.$

Calculation:

Plug the value of $x=2$ in $g\left(x\right)=x+7.$

  $\begin{array}{l}g\left(2\right)=2+7\\ g\left(2\right)=9\end{array}$

Thus, the value of $g\left(2\right)$ is 9.

e.

To determine

To find the value of $fog\left(2\right).$

Answer to Problem 2CE

The value of $fog\left(2\right)\text{ is }3.$

Explanation of Solution

Given two functions: $f:x\to \sqrt{x}\text{ and }g:x\to x+7.$

Calculation:

Plug the value of $x=2$

  $\begin{array}{l}\left(fog\right)\left(2\right)=f\left(g\left(x\right)\right)\\ =f\left(x+7\right)\\ =\sqrt{2+7}\\ =\sqrt{3x+1}\\ =3\end{array}$

Thus, the value of $fog\left(2\right)\text{ is }3.$

f.

To determine

To find the value of $\left(fog\right)\left(x\right).$

Answer to Problem 2CE

The value of $\left(fog\right)\left(x\right)\text{ is }\sqrt{x}+7.$

Explanation of Solution

Given two functions: $f:x\to \sqrt{x}\text{ and }g:x\to x+7.$

Calculation:

  $\begin{array}{l}\left(fog\right)\left(x\right)=f\left(g\left(x\right)\right)\\ =f\left(x+7\right)\\ =\sqrt{x}+7\end{array}$

Thus, the value of $\left(fog\right)\left(x\right)\text{ is }\sqrt{x}+7.$