Chapter 14.6, Problem 1CE

a.

To determine

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

Answer to Problem 1CE

The value of $f\left(4\right)$ is $5.$

Explanation of Solution

Given two functions: $f\left(x\right)=x+1\text{ and }g\left(x\right)=3x.$

Calculation:

Plug the value of $x=4$ in $f\left(x\right)=x+1.$

  $\begin{array}{l}f\left(4\right)=4+1\\ =5\end{array}$

Thus, the value of $f\left(4\right)$ is $5.$

b.

To determine

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

Answer to Problem 1CE

The value of $gof\left(4\right)$ is $15.$

Explanation of Solution

Given two functions: $f\left(x\right)=x+1\text{ and }g\left(x\right)=3x.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(x\right)=g\left(f\left(x\right)\right)\\ =g\left(x+1\right)\\ =3\left(x+1\right)\\ =3x+3\end{array}$

Now put the value of $x$

  $\begin{array}{l}\left(gof\right)\left(x\right)=3x+3\\ gof\left(4\right)=3\cdot 4+3\\ =12+3\\ =15\end{array}$

Thus, the value of $gof\left(4\right)$ is $15.$

c.

To determine

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

Answer to Problem 1CE

The value of $\left(gof\right)\left(x\right)\text{ is }3x+3.$

Explanation of Solution

Given two functions: $f\left(x\right)=x+1\text{ and }g\left(x\right)=3x.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(x\right)=g\left(f\left(x\right)\right)\\ =g\left(x+1\right)\\ =3\left(x+1\right)\\ =3x+3\end{array}$

Thus, the value of $\left(gof\right)\left(x\right)\text{ is }3x+3.$

d.

To determine

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

Answer to Problem 1CE

The value of $g\left(2\right)$ is 6.

Explanation of Solution

Given two functions: $f\left(x\right)=x+1\text{ and }g\left(x\right)=3x.$

Calculation:

Plug the value of $x=4$ in $g\left(x\right)=3x.$

  $\begin{array}{l}g\left(2\right)=3\cdot 2\\ =6\end{array}$

Thus, the value of $g\left(2\right)$ is 6.

e.

To determine

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

Answer to Problem 1CE

The value of $fog\left(2\right)\text{ is }7.$

Explanation of Solution

Given two functions: $f\left(x\right)=x+1\text{ and }g\left(x\right)=3x.$

Calculation:

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

Plug the value of $x=2$

  $\begin{array}{l}\left(fog\right)\left(x\right)=3x+1\\ fog\left(2\right)=3\cdot 2+1\\ =6+1\\ =7\end{array}$

Thus, the value of $fog\left(2\right)\text{ is }7.$

f.

To determine

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

Answer to Problem 1CE

The value of $\left(fog\right)\left(x\right)\text{ is }3x+1.$

Explanation of Solution

Given two functions: $f\left(x\right)=x+1\text{ and }g\left(x\right)=3x.$

Calculation:

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

Thus, the value of $\left(fog\right)\left(x\right)\text{ is }3x+1.$