Q. 34 - 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: $f\left(x\right)\le g\left(x\right)$

Step-by-Step Solution

Answer

Part (a)  $x=2$

Part (b) $\left\{x|x\le 2\right\}$

Part (a) Step 1. Given Information.

The graph is given 

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

Part (a). Step 2. Explanation.

The equation $f\left(x\right)=g\left(x\right)$ represents intersection of graphs.

So, $f\left(x\right)=g\left(x\right)$  is point $\left(2,5\right)$

Here, $x=2$ is the solution of $f\left(x\right)=g\left(x\right)$

Part (b). Step 1. Explanation

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

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

Point of intersection of $f\left(x\right)$and $g\left(x\right)$ is $\left(2,5\right)$.

So, for x less than equal to 2, the function $f\left(x\right)$is less than equal to $g\left(x\right)$.

The solution is $x\le 2$.