Chapter 6.3, Problem 4AGP

To determine

To plot: The graph of the given inequality.

Answer to Problem 4AGP

The graph of the given inequality is given below.

Explanation of Solution

Given:

The given inequality function is:

  $f\left(x\right)\ge \sqrt{2x+1}\dots \left(1\right)$

The value of what’s under the square root must be greater than equal to zero.

Therefore,

  $\begin{array}{c}2x+1\ge 0\\ x\ge \frac{-1}{2}\end{array}$

So the domain is $\left\{x:x\ge \frac{-1}{2}\right\}$ .

The table for the graph of the function $f\left(x\right)=\sqrt{2x+1}$ is given as:

$x$	$0$	$4$
$f\left(x\right)$	$1$	$3$

The graph of the given inequality function is given by:

  

Because $y$ is greater than, so the shaded region must be lies above the boundary of the graph and within the domain.

Check:

Select a point in the shaded region and verify it is a solution of the inequality.

Test for the point $\left(100,100\right)$

  $\begin{array}{c}100\ge \sqrt{2\left(100\right)+1}\\ 100\ge 14.17\left[\text{True}\right]\end{array}$