Question

1. If $g\left(x\right)=2x-1$, find $g\left(8\right)$ and $g\left(-8\right)$.
2. Find the image of 5.
3. Find the pre image of 7.

Short answer

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

(b) The image of 5 is 9.

(c) The preimage of 7 is 4.

Step-by-step solution

a.Step 1. Given Information.

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

Step 2. 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 $g\left(x\right)=2x-1$.

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

Step 3. Conclusion.

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

b.Step 1. Given Information.

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

Step 2. Explanation.

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, $g:5\to 9$.

Step 3. Conclusion.

Therefore, the image of 5 is 9.

c.Step 1. Given Information.

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

Step 2. Calculation.

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

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

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

Step 3. Conclusion.

Therefore, the preimage of 7 is 4.