Chapter 14.1, Problem 4CE

a.

To determine

To find: The value of $g\left(8\right)$ and $\text{g}\left(-8\right)$ if the function is $g\left(x\right)=2x-1$ .

Answer to Problem 4CE

The value of $g\left(8\right)$ is 15 and value of $g\left(-8\right)$ is $-17$ .

Explanation of Solution

Given information: The function is $g\left(x\right)=2x-1$ .

Calculation:

To find $g\left(8\right)$ , substitute 8 for x in the function $g\left(x\right)=2x-1$ .

  $\begin{array}{c}g\left(8\right)=2\left(8\right)-1\\ =16-1\\ =15\end{array}$

To find $g\left(-8\right)$ , substitute $-8$ for x in the function $g\left(x\right)=2x-1$ .

  $\begin{array}{c}g\left(-8\right)=2\left(-8\right)-1\\ =-16-1\\ =-17\end{array}$

Therefore, the value of $g\left(8\right)$ is 15 and value of $g\left(-8\right)$ is $-17$ .

b.

To determine

To find: The image of $5$ if the function is $g\left(x\right)=2x-1$ .

Answer to Problem 4CE

The image of 5 is 9.

Explanation of Solution

Given information: The function is $g\left(x\right)=2x-1$ .

Calculation:

To find the image of 5, substitute 5 for x in the function $g\left(x\right)=2x-1$ .

  $\begin{array}{c}g\left(5\right)=2\left(5\right)-1\\ =10-1\\ =9\end{array}$

So, $g:5\to 9$ .

Therefore, the image of 5 is 9.

c.

To determine

To find: The pre image of $7$ if the function is $g\left(x\right)=2x-1$ .

Answer to Problem 4CE

The preimage of 7 is 4.

Explanation of Solution

Given information: The function is $g\left(x\right)=2x-1$ .

Calculation:

For the preimage $g:x\to 2x-1$ and $2x-1=7$ .

Substitute 7 for x in the equation $2x-1=7$ .

  $\begin{array}{c}2x-1=7\\ 2x=7+1\\ x=\frac{8}{2}\\ x=4\end{array}$

Therefore, the preimage of 7 is 4.