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Chapter 3: Q. 77 (page 157)

In Problems 75鈥�80, for the given functions fand g.

(a) Graph fand gon the same Cartesian plane.

(b) Solvefx=gx.

(c) Use the result of part (b) to label the points of intersection of the graphs of fandg.

(d) Shade the region for which fx>gxthat is, the region below f and aboveg.

fx=-x2+4;gx=-2x+1.

Short Answer

Expert verified

(a) The graph fof andg

(b)x=3,x=-1.

(c) The point of intersection is3,-5,-1,3.

(d) The shaded region is,

Step by step solution

01

Part (a) Step 1. Given information

It is given thatfx=-x2+4;gx=-2x+1.We need to graph fand gon the same cartesian plane.

02

Step 2. Graph fx and gx

03

Part (b) Step 1. Given information

It is given thatfx=-x2+4;gx=-2x+1.We need to solvefx=gx.

04

Step 2. Solving

fx=gx.

-x2+4=-2x+1.

x2-2x-3=0.

x=+2卤-22-4路1路-32路1.

=+2卤4+122.

=+2卤162.

=2卤42.

x=2+42=3,

and x=2-42=-1.

The value of the functionfandgare equal whenx=3,-1.

05

Part (c) Step 1. Given information

It is given thatfx=-x2+4;gx=-2x+1.We need to use the result of part (b) to label the point of intersection.

06

Step 2. Simplify

Lety=fx=-x2+9.

y=gx=-2x+1.

Whenx=3,y=-2路3+1=5.

Whenx=-1,y=-2路-1+1=3.

The point of intersection is3,-5,-1,3.

07

Part (d) Step 1. Given information

It is given thatfx=-x2+4;gx=-2x+1.We need to draw the shaded region for whichfx>gx.

08

Step 2. Draw the shaded region

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