Final Radicals and rational exponents Solving radical equations

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Presentation transcript:

Final Radicals and rational exponents Solving radical equations Operations with Functions Inverse Functions 100 100 100 100 200 200 200 200 300 300 300 300 400 400 400 400 500 500 500 500

Write the following using radical notation Write the following using radical notation. Assume that all variables represent positive real numbers. X2/5

Simplify: 27 2/3

Simplify:

Simplify: 495/6 491/3

Simplify: X 1/3*X 1/4

Let f(x)=3x+2 and g(x)=2x-4. Find f(x) + g(x).

Let f(x)=3x+2 and g(x)=2x-4. Find g(x) - f(x).

Let f(x)=2x and g(x)=x+5. Find f(g(x)).

Let f(x)=5x and g(x)=x2. Find g(f(x)).

Let f(x)=3x+2 and g(x)=2x2-4. Find g(f(x)).

Solve: x3 - 5 = 59

Solve the equation and check for extraneous solutions.

Solve the equation and check for extraneous solutions.

Solve the equation and check for extraneous solutions.

The sales of a certain product after an initial release can be found by the equation S=14 + 61, where S represents the total sales and t represents the time in weeks after release. How many weeks will pass before the product sells about 175 units? Round your answer to the nearest week.

Find the Inverse of the relation f={(6,-9),(-9,6),(1,8)}. Part 1: Find the Inverse of the relation f={(6,-9),(-9,6),(1,8)}. Part 2: Find the Inverse of the relation g={(2,7),(7,2),(-6,-1)}.

Find the inverse of the relation Part 1: Find the inverse of the relation y = 4x + 2. Part 2: y = 2x + 4

Sketch the inverse of the graph

Sketch the inverse of the graph

Sketch the inverse of the graph

BONUS

The Volume of a sphere can be given by the formula V = 4.18879r3. You have to design a spherical container that will hold a volume of 65 cubic inches. What should the radius of your container be?

Final Jeopardy

Graph: F(x) =

2

495/6-1/3 = 491/2 = 7

x1/3*x1/4 = x1/3+1/4 = x4/12+3/12 = x7/12

3x+2+2x-4 =5x - 2

2x-4-(3x+2) = 2x-4-3x-2 = -x - 6

2(x + 5)= 2x + 10

(5x)2 = 25x2

2(3x + 2)2- 4 = 2(9x2 +12x + 4) - 4= 18x2 + 24x + 8 – 4= 18x2+24x+4

X3 – 5 = 59 X3 = 64 X = 4

2y-7 = 112 2y = 121+7 2y = 128 y = 64

X –7 = 53 X = 125 +7 = 132

(3x-8)1/2 = 5 ((3x-8)1/2)2 = (5)2 3x – 8 = 25 3x = 33 x = 11

Part 1: f-1={(-9,6),(6,-9),(8,1)} Part 2: g-1={(7,2),(2,7),(-1,-6)}

Part 1 Part 2:

Original  Inverse 

Original   Inverse

Original   Inverse