Chapter 8.1, Problem 42HP

To determine

To calculate: To find the value of the function $f\left[g\left(-8\right)\right]$

Answer to Problem 42HP

  $f\left[g\left(-8\right)\right]=-251$

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 $f\left[g\left(-8\right)\right]$ , let us first find $g\left(-8\right)$

  $\begin{array}{l}g\left(-8\right)=8\left(-8\right)+2\\ g\left(-8\right)=-64+2\\ g\left(-8\right)=-62\end{array}$

Now, $f\left[g\left(-8\right)\right]=f\left[-62\right]$

Thus, on evaluating $f\left(-62\right)$ ,

  $\begin{array}{l}f\left(-62\right)=4\left(-62\right)-3\\ f\left(-62\right)=-248-3\\ f\left(-62\right)=-251\end{array}$

Hence, $f\left[g\left(-8\right)\right]=-251$