Chapter 14.6, Problem 4WE

a).

To determine

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

Answer to Problem 4WE

The value of $koh:3\text{ is }25.$

Explanation of Solution

Given two functions: $h:x\to x^2-1\text{ and }k:x\to 2x+7.$

Calculation:

  $\begin{array}{l}koh:3=2{\left(3\right)}^2+7\\ koh:3=2\times 9+7\\ koh:3=18+7\\ =25\\ \text{finally }koh:3=25\end{array}$

Thus, the value of $koh:3\text{ is }25.$

b.

To determine

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

Answer to Problem 4WE

The value of $koh:5\text{ is }57$

Explanation of Solution

Given two functions: $h:x\to x^2-1\text{ and }k:x\to 2x+7.$

Calculation:

  $\begin{array}{l}koh:5=2{\left(5\right)}^2\text{+7 }\\ =2\times 25+7\\ =50+7\\ =57\end{array}$

Thus, the value of $koh:5\text{ is }57$

c.

To determine

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

Answer to Problem 4WE

The value of $koh:x\text{ is }2x^2+7.$

Explanation of Solution

Given two functions: $h:x\to x^2-1\text{ and }k:x\to 2x+7.$

Calculation:

  $koh:x=2x^2+7$

Thus, the value of $koh:x\text{ is }2x^2+7.$

d.

To determine

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

Answer to Problem 4WE

The value of $hok:3\text{ is }169.$

Explanation of Solution

Given two functions: $h:x\to x^2-1\text{ and }k:x\to 2x+7.$

Calculation:

  $\begin{array}{l}hok:3={\left(2\times 3+7\right)}^2\\ hok:3={\left(6+7\right)}^2\\ ={\left(13\right)}^2\\ =169\end{array}$

Thus, the value of $hok:3\text{ is }169.$

e.

To determine

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

Answer to Problem 4WE

The value of $hok:5\text{ is }289.$

Explanation of Solution

Given two functions: $h:x\to x^2-1\text{ and }k:x\to 2x+7.$

Calculation:

  $\begin{array}{l}hok:5={\left(2\times 5+7\right)}^2\\ ={\left(10+7\right)}^2\\ ={\left(17\right)}^2\\ =289\end{array}$

Thus, the value of $hok:5\text{ is }289.$

f.

To determine

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

Answer to Problem 4WE

The value of $hok:x\text{ is }4x^2+28x+49.$

Explanation of Solution

Given two functions: $h:x\to x^2-1\text{ and }k:x\to 2x+7.$

Calculation:

  $\begin{array}{l}hok:x={\left(2\cdot x+7\right)}^2\\ ={\left(2x+7\right)}^2\\ hok:x={\left(2x+7\right)}^2\\ =\left(2x+7\right)\cdot \left(2x+7\right)\\ =\left(2x\cdot 2x\right)+\left(2x\cdot 7\right)+\left(2x\cdot 7\right)+\left(7\cdot 7\right)\\ =4x^2+14x+14x+49\\ =4x^2+28x+49\end{array}$

Thus, the value of $hok:x\text{ is }4x^2+28x+49.$