Domain Algebraically

1. Warm-UpWarm-Up

2. Homework QuestionsHomework Questions

3. Domain AlgebraicallyDomain Algebraically
Pre-CalculusPre-Calculus
Mrs. RamseyMrs. Ramsey

4. Find the DomainFind the Domain


2
y x=
2
4y x= −

5. Find the domainFind the domain


2
( 2)y x= −
2
( 3) 7y x= − +

6. Find the domainFind the domain


2
6 1y x x= + −
2
4 9y x x= − −

7. Find the domainFind the domain


3
y x=
3 2
2 4 7y x x x= + − +

8. Find the domainFind the domain


y x=
8y x= −

9. Find the domainFind the domain


2 6y x= + −
4 1y x= − − +

10. Find the domainFind the domain
 2
5 6y x x= − +
2
7 12y x x= + +

11. Rational ProblemsRational Problems
 1
y
x
=
3
2
x
y
x
+
=
−

12. More Rational ProblemsMore Rational Problems
 
2
4
x
y
x
=
( 3)( 7)
7
x x
y
x
+ −
=
−

13. More Rational ProblemsMore Rational Problems
 
2
2
4
2
x
y
x x
−
=
− −
3
2
3
4
x
y
x
+
=
−

14. Rational ProblemsRational Problems
 3
5y x= + 5
6 1y x= − −

15. Log ProblemsLog Problems
 log( )y x= log( 3)y x= +

16. Log ProblemsLog Problems
 ln( )y x= ln( 6)y x= +

17. Exponential ProblemsExponential Problems
 
2x
y = ( 4)
3 1x
y −
= +

18. More Exponential ProblemsMore Exponential Problems
 1
6x
y −
= ( 2)
3 11x
y +
= − −

19. Finding the domain:Finding the domain:
 Let f(x) = xLet f(x) = x22
– 1 and g(x) =– 1 and g(x) =
 f(g(x))f(g(x)) g(f(x))g(f(x))

 Domain is [0,Domain is [0, ∞)∞) D: (-D: (- ∞∞ , -1]U[1,, -1]U[1, ∞∞ ))
x
( )
2
1x − 2
1x −
2
1 0x − ≥

20. Find the domainFind the domain
11.11. Find f(g(x)) and g(f(x)) and state domain:Find f(g(x)) and g(f(x)) and state domain:
( ) 3 2
( ) 1
f x x
g x x
= +
= −

21. Find the domainFind the domain
12.12. Find f(g(x)) and g(f(x)) and state domain:Find f(g(x)) and g(f(x)) and state domain:
2
( ) 1
1
( )
1
f x x
g x
x
= −
=
−

22. Find the domainFind the domain
13.13. Find f(g(x)) and g(f(x)) and state domain:Find f(g(x)) and g(f(x)) and state domain:
2
( ) 2
( ) 1
f x x
g x x
= −
= +

23. Find the domainFind the domain
14.14. Find f(g(x)) and g(f(x)) and state domain:Find f(g(x)) and g(f(x)) and state domain:
1
( )
1
( )
f x
x
g x x
=
−
=

24. Also state the domain:Also state the domain:

25. Also state the domain:Also state the domain:

26. HomeworkHomework
 Domain WorksheetDomain Worksheet