Q. 33 - Precalculus Enhanced with Graphing Utilities

Question

In parts (a) and (b) use the following figure

(a) Solve the equation: $f\left(x\right)=g\left(x\right)$.

(b) Solve the inequality: $f\left(x\right)>g\left(x\right)$.

Step-by-Step Solution

Answer

Part (a) $x=-4$

Part (b) $\left\{x|x<-4\right\}$

Part (a) Step 1. Given Information.

The graph is given

Answer the questions.

Part (a). Step 2. Explanation.

There are two graphs $f\left(x\right), g\left(x\right)$. Intersecting at point $\left(-4,6\right)$.

Also, $f\left(x\right)=g\left(x\right)$ represents intersection of graphs.  

So, $f\left(x\right)=g\left(x\right)$ is point $\left(-4,6\right)$

So, $x=-4$

Part (b). Step 1. Explanation.

In graph $f\left(x\right)$ values of y are decreasing as respective values of x are increasing. so $f\left(x\right)$ is decreasing.

In graph $g\left(x\right)$ values of y are increasing as respective values of x are increasing .  so, g(x) is increasing .

Part (b). Step 2. Conclusion.

Intersection of $f\left(x\right)$and $g\left(x\right)$ is $\left(-4,6\right)$.

Hence, for $x<-4$, $f\left(x\right)>g\left(x\right)$