Power Point Slides for team teaching lesson on Solving inequalities that involve radical functions.

1. November 28, 2013

2.  to solve inequalities that involve radical
functions

3.  A radical function looks like
n y
radicant
index
 When , we have a square root fuction.
n  2
n  3
 When , we have a cube root function.
 When , we have a fourth root function.
n  4
 When n  5
, we have a fifth root function,
and so on…

4. Given a radical function ,
Case 1:
If n is even, then and
Case 2:
If n is odd, then and
Furthermore,
n y
0 n y  0y 
n y R yR
 n
n y  y

5.  Which of the following equations does not
have a solution? Why?
Because
x  2  0

6.  What can you say about the solutions of the
following inequalities?
4
8
x
3  5  
2
  
3
x
x
2  4  
2

7.  Do the following inequalities have solutions?
What is the lower bound for each of the
inequalities?
4
3 5
3
1 3
x
x
x
 
 
 
x
0   3 
5
4
x
0   
3
x
0   1 
3
Solve the inequalities.

8.  Suppose the following inequalities are valid,
then what must be true about each of the
inequalities?
4 2
6
x x
6 5
3 6
1
x
x
  
  
  
4 2
6
x x
6 0
3 0
0
x
x
 
 
 
Solve the inequalities.

9.  Let’s solve the following inequalities
4
2 3 3
3 2 5
2 4
2
x
x
x
x
 
 
 
 

10.  Up until now, we have discussed the fact
that for
Case 1:
If
k
f x g x
a if g x then
b if g x and f x then f x g x
Case 2:
If
n  2k
2
2
( ) ( )
( ) ( ) 0,
( ) ( ) 0 ( ) 0, ( ) k
( )

 
  
2
k
f ( x ) g ( x
)
a if g x then f x
b if g x then f x g 2
x
( ) ( ) 0, ( ) 0
( ) ( ) 0, ( ) k
( )

 
 

11.  Do you remember the fact that if ,
then and ?
n yR y R 
 Because of this, we have less rules for solving
inequalities whose index is odd.
 In fact,
n  2k 1
k k
2  1 2 
1
f x g x f x g x
( )  ( )  ( ) 
( )
k k
2  1 2 
1
f x g x f x g x
( )  ( )  ( ) 
( )

12.  Solve each of the following inequalities whose
index is odd.
3
 
2 2
3
9 2
1  2  
3
1
1
x
x
x
x

 
Answers:
[1, )
( 14, 14)


 
    
 
 
1
0,
2
x