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

Quiz Are the following functions inverses of each other ? (hint: you must use a composition each other ? (hint: you must use a composition to prove it). to prove it). (-2, 5), (5, 6), (-2, 6), (7, 6) What is the inverse relation of: Find the inverse of: y = 0.5x

Section 6-6 Solve Radical Functions

Vocabulary Radical Equation: An equation with a radical symbol in it. symbol in it.

Review (Solving single variable equations) 10 = 3x – 2 What does it mean to solve an equation ? “use properties of equality to get the variable on one side of the equal sign variable on one side of the equal sign and every other number on the other side.” and every other number on the other side.” = 3x 12 = 3x ÷ 3 4 = x

Your Turn: Solve for ‘x’ 1. 2.

Now solve a radical equation. Remove the radical by squaring each side x = 3 Isolate ‘x’ on one side of the equal sign by of the equal sign by subtracting 6 from both sides. subtracting 6 from both sides.

Using Exponent Form (may be easier) Convert to Exponent Form Use “power of a power” to turn the exponent into to turn the exponent into a ‘1’ a ‘1’ x = 3

Another example: Subtract ‘1’ from each side Cube each side Add ‘5’ to each side

Your Turn: 3. 4.

Vocabulary Extraneous Solution: 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? Your turn: 5. Simplify the above product.

Equations with two radicals Since 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 one of the radicals (by squaring it) then we could then solve the equation. it) then we could then solve the equation. Square both sides.

Equations with two radicals F.O.I.L. Combine like terms

Equations with two radicals Try to get the radical all by itself Square both sides

Equations with two radicals Factor Solve using zero product property Write quadratic in standard form.

Equations with two radicals Check for extraneous solutions. Check: x = 3 ? ? x = 3 is extraneous Check: x = -2 ?? x = -2 is the only solution

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