Q 5.87 - Intermediate Algebra

Question

For function $f\left(x\right)=x^2-5x-24$ and $g\left(x\right)=x+3$ find (a) $\left(\frac{f}{g}\right)\left(x\right)$ (b) $\left(\frac{f}{g}\right)\left(-3\right)$

Step-by-Step Solution

Answer

The solution is (a) $x-8$

(b) The value at $x=-3$ is $-11$

Step 1. Given information

$f\left(x\right)=x^2-5x-24$ and $g\left(x\right)=x+3$

Part (a) Step 1. Find f g x

$$\begin{gathered} \left(\frac{f}{g}\right)\left(x\right)=\frac{x^2-5x-24}{x+3} \\ \left(\frac{f}{g}\right)\left(x\right)=x-8 \end{gathered}$$

Part (b) Step 1. Substitute x = - 3

$$\begin{gathered} \left(\frac{f}{g}\right)\left(x\right)=x-8 \\ \left(\frac{f}{g}\right)\left(-3\right)=\left(-3\right)-8 \\ \left(\frac{f}{g}\right)\left(-3\right)=-11 \end{gathered}$$