Q 5.88 - Intermediate Algebra

Question

For function $f\left(x\right)=x^2-5x-36$ and $g\left(x\right)=x+4$ Find (a) $\left(\frac{f}{g}\right)\left(x\right)$  (b) $\left(\frac{f}{g}\right)\left(-5\right)$

Step-by-Step Solution

Answer

The solution is (a) $x-9$

(b) The value at $x=-5$ is $-14$

Step 1. Given Information

$f\left(x\right)=x^2-5x-36$ and $g\left(x\right)=x+4$

Part (a) Step 1. Find f g x

$$\begin{gathered} \left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)} \\ \left(\frac{f}{g}\right)\left(x\right)=\frac{x^2-5x-36}{x+4} \\ \left(\frac{f}{g}\right)\left(x\right)=x-9 \end{gathered}$$

Part (b) Step 1. Substitute x = - 5

$$\begin{gathered} \left(\frac{f}{g}\right)\left(x\right)=x-9 \\ \left(\frac{f}{g}\right)\left(-5\right)=\left(-5\right)-9 \\ \left(\frac{f}{g}\right)\left(-5\right)=-14 \end{gathered}$$