Tonight’s Homework:

6-66-6: (page 456): (page 456) (evens): 4 – 18, 24, 28, 32 – 38, 46, 50, 58(evens): 4 – 18, 24, 28, 32 – 38, 46, 50, 58 (17 points)(17 points)

Quiz 6-4

1.1.

2.2.

4. Are the following functions inverses of 4. Are the following functions inverses of each other ? (hint: you must use a each other ? (hint: you must use a compositioncomposition to prove it).to prove it).

(-2, 5), (5, 6), (-2, 6), (7, 6)(-2, 5), (5, 6), (-2, 6), (7, 6)

What is the inverse relation of:What is the inverse relation of:

Find the inverse of: y = 0.5x + 2Find the inverse of: y = 0.5x + 2

?)(1 xf2)( xxf

3.3.

42)( xxf 22)( xxg

Section 6-6

Solve Radical FunctionsSolve Radical Functions

Vocabulary

Radical EquationRadical Equation: An equation with a radical : An equation with a radical symbol in it. symbol in it. 3 25 x

Review (Solving single variable equations)

10 = 3x – 2 10 = 3x – 2

What does it mean to solve an equation ?What does it mean to solve an equation ?

““use properties of equality to get theuse properties of equality to get the variable on one side of the equal signvariable on one side of the equal sign and every other number on the other side.”and every other number on the other side.”

+ 2+ 2+ 2+ 2

12 = 3x12 = 3x

÷ 3÷ 3÷ 3÷ 34 = x4 = x

Your Turn:

Solve for ‘x’Solve for ‘x’

1.1. 25)3( 2 x

2. 2. 27)1( 3 x

Now solve a radical equation.

Remove the radical Remove the radical by squaring each sideby squaring each side

36 x

2236 x

96x-6-6 -6-6

x = 3x = 3

Isolate ‘x’ on one side Isolate ‘x’ on one side of the equal sign by of the equal sign by subtracting 6 from subtracting 6 from bothboth sides. sides.

Using Exponent Form (may be easier)

36 x

36 21

x Convert to Exponent FormConvert to Exponent Form

22

21

36 xUse “power of a power”Use “power of a power” to turn the exponent intoto turn the exponent into a ‘1’a ‘1’

222

36 x

96x x = 3x = 3

Another example:

1153 x

253 x

-1-1 -1-1Subtract ‘1’ from each sideSubtract ‘1’ from each side

Cube each sideCube each side

333 25 x

85 x3x

Add ‘5’ to each sideAdd ‘5’ to each side

Your Turn:

3. 3. 1643 32

x

4.4. 53212 34

x

Vocabulary

Extraneous SolutionExtraneous Solution: a solution that, when : a solution that, when plugged back into the original equation,plugged back into the original equation, does not make a true statement.does not make a true statement.

How would you do this?

?5151 xx

?512x

251515)1( xxx

Your turn:Your turn:

5. Simplify the above product.5. Simplify the above product.

Equations with two radicals

xx 31026 Since they are not “like” radicalsSince they are not “like” radicals (same radicand and index number) (same radicand and index number) you can’t just combine them.you can’t just combine them.

If we got rid of If we got rid of oneone of the radicals (by squaring of the radicals (by squaring it) then we could then solve the equation.it) then we could then solve the equation.

2231026 xx Square both sides.Square both sides.

xxx 3102626

Equations with two radicals

xxx 3102626

xxxx 310462626

xxx 3106410

F.O.I.L.F.O.I.L.

Combine like termsCombine like terms

Equations with two radicals

xxx 3106410

xx 464 xx 6

Try to get the radical all by itselfTry to get the radical all by itself

Square both sidesSquare both sides

22)6( xx 26 xx

Equations with two radicals

FactorFactor

062 xx

Solve using Solve using zero product propertyzero product property

26 xx Write quadratic in standard form.Write quadratic in standard form.

0)2)(3( xx

2,3 x

Equations with two radicals2,3 x

)3(310263

)2(310262

Check for extraneous solutions.Check for extraneous solutions.

Check: x = 3Check: x = 3

?? 123 ??

x = 3 is x = 3 is extraneousextraneous

Check: x = -2Check: x = -2??

xx 31026

1624 ??

x = -2 is the x = -2 is the onlyonly solution solution

Your turn:

6. 6. 5143 xx

Step 1: Square each side Step 1: Square each side Step 2: combine like termsStep 2: combine like termsStep 3: Get the remaining radical by itselfStep 3: Get the remaining radical by itselfStep 4: Square both sides to remove the radicalStep 4: Square both sides to remove the radicalStep 5: Solve for ‘x’Step 5: Solve for ‘x’Step 6: Check for extraneous solutions.Step 6: Check for extraneous solutions.