Chapter 14.6, Problem 2WE

a.

To determine

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

Answer to Problem 2WE

The value of $\left(gof\right)\left(2\right)\text{ is }-2.$

Explanation of Solution

Given two functions: $f\left(x\right)=3x+1\text{ and }g\left(x\right)=x-9.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(2\right)=g\left(f\left(2\right)\right)\\ =g\left(3\cdot 2+1\right)\\ =g\left(6+1\right)\\ =g\left(7\right)\\ =7-9\\ =-2\end{array}$

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

b.

To determine

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

Answer to Problem 2WE

The value of $\left(gof\right)\left(x\right)\text{ is }3x-8.$

Explanation of Solution

Given two functions: $f\left(x\right)=3x+1\text{ and }g\left(x\right)=x-9.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(x\right)=g\left(f\left(x\right)\right)\\ =g\left(3x+1\right)\\ =\left(3x+1\right)-9\\ =3x-8\end{array}$

Thus, the value of $\left(gof\right)\left(x\right)\text{ is }3x-8.$

c.

To determine

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

Answer to Problem 2WE

The value of $\left(fog\right)\left(2\right)\text{ is }-20.$

Explanation of Solution

Given two functions: $f\left(x\right)=3x+1\text{ and }g\left(x\right)=x-9.$

Calculation:

  $\begin{array}{l}\left(fog\right)\left(2\right)=f\left(g\left(2\right)\right)\\ =f\left(2-9\right)\\ =f\left(-7\right)\\ =3\left(-7\right)+1\\ =-21+1\\ =-20\end{array}$

Thus, the value of $\left(fog\right)\left(2\right)\text{ is }-20.$

d.

To determine

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

Answer to Problem 2WE

The value of $fog\left(x\right)\text{ is }3x-26.$

Explanation of Solution

Given two functions: $f\left(x\right)=3x+1\text{ and }g\left(x\right)=x-9.$

Calculation:

  $\begin{array}{l}fog\left(x\right)=f\left(g\left(x\right)\right)\\ =f\left(x-9\right)\\ =3\left(x-9\right)+1\\ =3x-26\end{array}$

Thus, the value of $fog\left(x\right)\text{ is }3x-26.$