Chapter 14.6, Problem 3WE

a.

To determine

To find the value of $koh:3\to ?.$

Answer to Problem 3WE

The value of $koh:3\text{ is }8$ .

Explanation of Solution

Given two functions: $h:x\to \frac{x+1}{2}\text{ and }k:x\to x^3.$

Calculation:

  $\begin{array}{l}koh:3={\left(\frac{3+1}{2}\right)}^3\\ koh:3={\left(\frac{4}{2}\right)}^3\\ koh:3={\left(2\right)}^3\\ koh:3=8\end{array}$

Thus, the value of $koh:3\text{ is }8.$

b.

To determine

To find the value of $koh:5\to ?.$

Answer to Problem 3WE

The value of $koh:5\text{ is }27.$

Explanation of Solution

Given two functions: $h:x\to \frac{x+1}{2}\text{ and }k:x\to x^3.$

Calculation:

  $\begin{array}{l}koh:5={\left(\frac{5+1}{2}\right)}^3\\ =\frac{6}{2}\\ ={\left(3\right)}^3\\ =27\end{array}$

Thus, the value of $koh:5\text{ is }27.$

c.

To determine

To find the value of $koh:x\to ?.$

Answer to Problem 3WE

The value of $koh:x\text{ is }{\left(\frac{x+1}{2}\right)}^3.$

Explanation of Solution

Given two functions: $h:x\to \frac{x+1}{2}\text{ and }k:x\to x^3.$

Calculation:

  $koh:x={\left(\frac{x+1}{2}\right)}^3$

Thus, the value of $koh:x\text{ is }{\left(\frac{x+1}{2}\right)}^3.$

d.

To determine

To find the value of $hok:3\to ?.$

Answer to Problem 3WE

The value of $hok:3\text{ is }14.$

Explanation of Solution

Given two functions: $h:x\to \frac{x+1}{2}\text{ and }k:x\to x^3.$

Calculation:

  $\begin{array}{l}hok:3=\frac{3^3+1}{2}\\ hok:3=\frac{27+1}{2}\\ =\frac{28}{2}\\ =14\end{array}$

Thus, the value of $hok:3\text{ is }14.$

e.

To determine

To find the value of $hok:5\to ?.$

Answer to Problem 3WE

The value of $hok:5\text{ is }63.$

Explanation of Solution

Given two functions: $h:x\to \frac{x+1}{2}\text{ and }k:x\to x^3.$

Calculation:

  $\begin{array}{l}hok:5=\frac{5^3+1}{2}\\ =\frac{125+1}{2}\\ =\frac{126}{2}\\ =63\end{array}$

Thus, the value of $hok:5\text{ is }63.$

f.

To determine

To find the value of $hok:x\to ?.$

Answer to Problem 3WE

The value of $hok:x\text{ is }\frac{x^3+1}{2}.$

Explanation of Solution

Given two functions: $h:x\to \frac{x+1}{2}\text{ and }k:x\to x^3.$

Calculation:

  $hok:x=\frac{x^3+1}{2}$

Thus, the value of $hok:x\text{ is }\frac{x^3+1}{2}.$