P.o.D. – Find an equation for the inverse
of the function with the given equation.
1.) 𝑦 =
1
𝑥
1
2.) 𝑦 = 𝑥 + 7
2
3.) 𝑦 = 𝑥 3 − 2
1.) 𝑥 =
𝑓
1
𝑦
−1 (
1
→ 𝑥𝑦 = 1 → 𝑦 = →
𝑥) =
𝑥
1
𝑥
1
2.) 𝑥 = 𝑦 + 7 → 2𝑥 = 𝑦 + 14 →
2
2𝑥 − 14 = 𝑦 → 𝑓 −1 (𝑥 ) = 2𝑥 − 14
3.) 𝑥 = 𝑦 3 − 2 → 𝑥 + 2 = 𝑦 3 →
3
√𝑥 + 2 = 𝑦 → 𝑓 −1 (𝑥 ) =
3
√𝑥 + 2 𝑜𝑟 (𝑥 + 2)
1
3
8-4: Radical Notation for nth Roots
Learning Target: I will be able to
evaluate radicals and solve real-world
problems that can be modeled by
equations with radicals.
Recall: a square root symbol, √ , is also
known as a radical sign.
𝑛
Definition of √𝑥 :
When x is nonnegative and n is an
1
𝑛
𝑛
integer ≥ 2, then √𝑥 = 𝑥 .
Examples:
2
√𝑥 = √𝑥 =
3
1
𝑥3
5
1
𝑥5
√𝑥 =
√𝑥 =
7
√𝑥 5 =
10
√𝑥 4
=
4
𝑥 10
=
1
𝑥2
5
𝑥7
2
𝑥5
5
= √𝑥 2
The Geometric Mean:
Multiply all the numbers in a set and
take the nth root of the product.
EX: In a water quality survey, 8 samples
give the following levels of E-coli
bacteria.
Sample 1
Count 1
(per
100
mL)
2
57
3
173
4
40
5
577
6
7
1159 301
8
94
Use the geometric mean to compute the
average level of bacteria.
8
√1 ∙ 57 ∙ 173 ∙ 40 ∙ 577 ∙ 1159 ∙ 301 ∙ 94
8
= √7463362712502480
= 96.4088
EX: The following chart shows the
population for eight 1-square-mile
regions in the United States.
Sample
Population
1
47
2
68
3
159
4
2215
5
8715
6
10512
7
12130
8
45312
Use the geometric mean to compute an
average population density.
8
√47 ∙ 68 ∙ 159 ∙ 2215 ∙ 8715 ∙ 10512 ∙ 12130 ∙ 45312
8
= √56676679928852478824448000 = 1656
4
EX: Use a calculator to evaluate √2401.
There are two methods for doing this.
Root of a Power Theorem:
𝑛
√𝑥 𝑚 =
𝑚
𝑥𝑛
EX: Rewrite √√√√10 using rational
exponents.
(show work on the whiteboard)
1
1016
Upon completion of this lesson, you
should be able to:
1. Compute a geometric mean.
2. Evaluate nth roots.
3. Apply the Root of a Power Theorem
(make roots into fractional
exponents).
For more information, visit
http://hotmath.com/help/gt/genericalg2/section_7_6.ht
ml
HW
Pg.541
1-18, 21-29
Quiz 8.1-8.4 tomorrow