Chapter 3.1, Problem 33AYU

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: $f\left(x\right)>g\left(x\right)$.

To determine

To calculate: Solve the following function:

a. $f(x)=g(x)$

b. $f(x)>g(x)$

Answer to Problem 33AYU

Solution:

a. $x=-4$

b. $x>-4$

Explanation of Solution

Given:

The given figure is

Formula Used:

The points in a graph are written in the form $\left(x,f(x)\right)$.

The equilibrium point of 2 functions is the point at which the functions are equal and therefore, the 2 functions meet at the equilibrium point.

Calculation:

a. We have to solve the equation $f(x)=g(x)$

From the graph, we can see that $(-4,6)$ is the equilibrium point.

Therefore, at $(-4,6)$, we have $f(x)=g(x)$.

Thus, on solving the given equation, we get the solution as $x=-4$.

b. We have to solve the equation $f(x)>g(x)$.

We have solved that when $f(x)=g(x)$, we get $x=-4$.

Therefore, when $f(x)>g(x)$, we get $x>-4$.