This document contains homework questions from Mrs. Ramsey's pre-calculus class. It includes exercises to find the domain of various algebraic expressions and functions, including rational, logarithmic, and exponential functions. Students are asked to compute compositions of functions f(g(x)) and g(f(x)) and state their domains for different functions defined piecewise or implicitly. The document provides practice working with domains, an important concept in pre-calculus.

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