Algebra II 6

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√36 = 6

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3√(1/8)-1 = 3√8 = 23√274 = 34 = 81

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3√64 = 3√4*4*4 = 4√36x4 = √2*2*3*3*x*x*x*x = √(2*2)*(3*3)*(x*x)*(x*x) = 2*3*x*x = 6x2

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3.16

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61/2 + 1/3 63/6 + 2/6

65/6

(271/3)2 (61/4)2 272/361/2

961/2

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43-1/3w3-1/3 4-1w-1

¼ 1/w 1/(4w) t1-3/4

t1/4

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3√25*5 = 3√125 = 53√32x/4x = 3√8 = 2

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4√2*2*2*2*2*2 = 4√(2*2*2*2)*2*2 = 24√4

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4√7/4√8 = 71/4/81/4 = 71/4*83/4/81/4*83/4 = 4√(7*83)/8 = 4√((2*2*2*2)*(2*2*2*2)*2*7)/8 = 2*2*4√(2*7)/8 = 4√14/2

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3r1-1/4s2/3t0—3 = 3r3/4s2/3t3

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2(43/4)

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3√3*3*3*3 - 3√3 = 3 3√3 - 3√3 = 2 3√3

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3x1/2 –1 D: x 0x1/2 – 1 D: x 02x – x1/2 D: x 0(2x1/2 – 1)/x1/2 D: x > 0

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Where the x is in f put the g function f(g(x)) = 2(x2) + 3Simplify f(g(x)) = 2x2 + 3Example: Find g(f(x))

g(f(x)) = g(2x + 3) = (2x + 3)2 = 4x2 + 12x + 9

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ANS: [f g](x) = 6 – 2((6 - x)/2) = 6 – 2(3 – x/2) = 6 – 6 + x = x[g f](x) = (6 – (6 – 2x))/2 = (6 – 6 + 2x)/2 = 2x/2 = xyes they are inverses

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f-1(x) = {(3, 2), (5, 4)} – yes the inverse is a function

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√x domain x≥0; range y≥03√x domain x all real numbers; range y all real numbers

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Show graphs of y=√xy=2√xy=3√xy=1/2√xy=-2√xy=-√x

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36

3 right and 4 up3 left and 5 down

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Moved 4 left and 1 down so Domain: x ≥ 4; Range: y ≥ -1Cube roots always have Domain: all real numbers and Range: all real numbers

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5=4√x 54 = x x = 625

x4/3 = 81 x = +-813/4 = +-27

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√(2x+8) = 10 2x+8 = 100 2x = 92 x = 46

√(4x+28) = 3√(2x) 4x+28 = 9(2x) 4x+28 = 18x 28 = 14x x = 2

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(x+2)2 = 2x+28 x2+4x+4 = 2x+28 x2 +2x -24 = 0 (x+6)(x-4) = 0 x = -6, 4Check-6: -6+2 = √(2(-6)+28) -4=√(-12+28) -4 = 4 False4: 4+2 = √(2(4)+28) 6 = √36 6=6 True

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