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
=
−
=