Chapter 3.1, Problem 34AYU

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

To determine

To calculate: Solve the following function by using the giving graph

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

b. $f(x)\le g(x)$

Answer to Problem 34AYU

Solution:

a. $x=2$

b. $x\le 2$

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 $(2,5)$ is the equilibrium point.

Therefore, at $(2,5)$, we have $f(x)=g(x)$.

Thus, on solving the given equation, we get the solution as $x=2$.

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

We have solved that when $f(x)=g(x)$, we get $x=2$.

Therefore, when $f(x)\le g(x)$, we get $x\le 2$.