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Chapter 4: Q. 75 (page 242)

In Problems 75, determine where the graph of fis below the graph of gby solving the inequality f(x)鈮�g(x). Graph fand gtogether.

f(x)=x4-4g(x)=3x2

Short Answer

Expert verified

The graph is shown below:

Step by step solution

01

Given information

The given function are shown below:

f(x)=x4-4g(x)=3x2

02

Determine the intersection point. 

For intersection point, fx=gx.

x4-4=3x2x4-3x2-4=0x4-4x2+x2-4=0x2x2-4+1x2-4=0x2+1x2-4=0x2+1x-2x+2=0x=2,-2

x2+1 given the imaginary solution.

03

Graph the function fx

Sketch the graph of y=f(x)having vertex at (0,-4)and range [-4,鈭�).

04

Graph the function gx

Sketch the graph of y=gxhaving vertex at 0,0and range [0,鈭�).

05

Determine the shaded portion which satisfy the given inequality.

The portion where f(x)=x4-4less than or equal to g(x)=3x2is in the interval of [-2,2]as shaded in the following figure.

06

Write the conclusion

The final graph is shown below:

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