Intermediate Algebra Skill
Finding the Inverse of a Reciprocal Function
Find the inverse of the given function:
1) f ( x) = 1
x 1
2) f ( x) = 1 +1
x 1
3) f ( x) = 3
x+2
4) g ( x) = 3 3
x
5) g ( x) = 1
x+3
6) g ( x) = 4 1
x 1
7) h( x) = 2 +1
x +1
8) h( x)
Intermediate Algebra Skill
Finding the Domain: Given the Equation; Evenindexed Radical Function and
Quadratic Radicand
Find the Domain.
1) F ( x) = x2 9
2) G( x) = x 1 x2
3) f ( x) = x2 + 2 x 3
4) g ( x) = x 2 x2 x 1
5) H ( x) = x2 + 5x + 6
6) h( x) = 5
Intermediate Algebra Skill
Finding the Domain and Range of the Exponential Function Based on the Graph
Find the domain and Range of each graph:
1)
8 y
6
4
2
x
0
14
12
10
8
6
4
2
0
2
4
6
8
10
12
14
2
4
6
8
10
12
14
2
4
6
8
2)
8 y
6
4
2
x
0
14

Intermediate Algebra Skill
Finding the Inverse of a Function: Given as Ordered Pairs
Find the inverse of the given function:
1) f = (1,3) , ( 2,5) , ( 1, 1)
2) g = (9,5) , ( 2,10) , ( 1,7 )
3) F = ( 2,3) , (3,6) , ( 4,5)
4) G = ( 1,0) , ( 2,8) , ( 0,2)
5)
Intermediate Algebra Skill
Finding the Domain and the Range of a Function and its Inverse Based on their
Graphs
Find the domain and range of the function and its inverse from their graphs:
1)
4
y
2
x
0
6
4
2
0
2
4
6
2
4
6
2
4
6
2
4
2)
4
y
2
x
0
6
4
Intermediate Algebra Skill
Finding the Inverse of a Quadratic Function with Restricted Domain
Find the inverse of the given function:
1) f ( x) = x2 3; ( x 0)
2) f ( x) = x2 + 5; ( x 0)
3) f ( x) = x2 +1; ( x 0)
4) g ( x) = 1 x2; ( x 0)
5) g ( x) = x2 ; (
Intermediate Algebra Skill
Finding the Inverse of a Square Root Function
Find the inverse of the given function:
1) f ( x) = x
2) f ( x) = x +1
3) f ( x) = x 1
4) g ( x) = x 1 1
5) g ( x) = x + 2 +1
6) g ( x) = 4 4 x
2
7) h( x) = x +1
2
8) h( x) = 2 + 4 x
Intermediate Algebra
SkillBuilder # AE  1
Removing Nested Symbols of Grouping
Strategy: Repeatedly apply the distributive property of multiplication over addition
and
combine like terms, starting from the innermost quantity, and work your way
out.
Examp
Intermediate Algebra Skill
Finding the Inverse of a Rational Function
Find the inverse of the given function:
1) f ( x) = x +1
x 1
2) f ( x) = x 1
x
3) f ( x) = x
x 1
4) g ( x) = x 2
x+3
5) g ( x) = x +1
x
6) g ( x) = 2 x +1
x
7) h( x) = x 3
x2
8) h( x) =
Intermediate Algebra Skill
Finding the Domain: Given the Equation; Rational Function and Linear
Denominator
Find the Domain.
1) F ( x) = 1
x4
2) G( x) =
5
2x 6
3) f ( x) = 3
x +1
4) g ( x) = 7
x+3
5) H ( x) = x
x+2
6) h( x) = x
x2
7) J ( x) = x 2
x+4
8) j