Chapter 8.1, Problem 43HP

To determine

To calculate: To find the value of the function $g\left[f\left(12\right)\right]$

Answer to Problem 43HP

  $g\left[f\left(12\right)\right]=362$

Explanation of Solution

Given information: Functions are $f\left(x\right)=4x-3$ and $g\left(x\right)=8x+2$

Calculation:

Given the following functions:

  $f\left(x\right)=4x-3$

  $g\left(x\right)=8x+2$

Now, in order to evaluate $g\left[f\left(12\right)\right]$ , let us first find $f\left(12\right)$

  $\begin{array}{l}f\left(12\right)=4\left(12\right)-3\\ f\left(12\right)=48-3\\ f\left(12\right)=45\end{array}$

Now, $g\left[f\left(12\right)\right]=g\left[45\right]$

Thus, on evaluating $g\left(45\right)$ ,

  $\begin{array}{l}g\left(45\right)=8\left(45\right)+2\\ g\left(45\right)=360+2\\ g\left(45\right)=362\end{array}$

Hence, $g\left[f\left(12\right)\right]=362$