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Chapter 4: Q. 76 (page 242)

In Problems 76, determine where the graph of fis below the graph of gby solving the inequality f(x)鈮�g(x). Graph fand gtogether.

fx=x4gx=2-x2

Short Answer

Expert verified

The graph is shown below:

Step by step solution

01

Given information

The given functions are shown below:

fx=x4gx=2-x2

02

Determine the intersection point.

For intersection point,fx=gx

role="math" localid="1649315638482" x4=2-x2x4+x2-2=0x4+2x2-x2-2=0x2x2+2-1x2+2=0x2-1x2+2=0x-1x+1x2+2=0x=1,-1

x2+2 gives the imaginary solution.

03

Graph the function fx

Sketch the graph of y=f(x)having vertex at (0,0)and range [0,鈭�).

04

Graph the function gx

Sketch the graph of y=g(x)having vertex at (0,2)and range (-鈭�,2].

05

Determine the shaded portion which satisfy the given inequality.

The portion where f(x)=x4less than or equal tog(x)=2-x2is in the interval of [-1,1]as shaded in the following figure.

06

Write the conclusion

The final graph is shown below:

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