Algebra II 6
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√36 = 6
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3√(1/8)-1
3√274
= 3√8 = 2
= 34 = 81
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3√64
= 3√4*4*4 = 4
= √2*2*3*3*x*x*x*x = √(2*2)*(3*3)*(x*x)*(x*x) = 2*3*x*x = 6x2
√36x4
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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  272/361/2  961/2
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 43-1/3w3-1/3  4-1w-1  ¼  1/w  1/(4w)
 t1-3/4  t1/4
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3√25*5
= 3√125 = 5
= 3√8 = 2
3√32x/4x
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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
= 4√14/2
2*2*4√(2*7)/8
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5√x5/5√(y2)5 =
x/y2
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
x1/2 – 1
2x – x1/2
(2x1/2 – 1)/x1/2 D: x > 0
D: x  0
D: x  0
D: x  0
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Where the x is in f put the g function
f(g(x)) = 2(x2) + 3
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Simplify
f(g(x)) = 2x + 3
Example: 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 = x
yes 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≥0
3√x  domain x all real numbers; range y all real numbers
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Show graphs of
y=√x
y=2√x
y=3√x
y=1/2√x
y=-2√x
y=-√x
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3 right and 4 up
3 left and 5 down
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Moved 4 left and 1 down so  Domain: x ≥ 4; Range: y ≥ -1
Cube 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, 4
Check
-6: -6+2 = √(2(-6)+28)  -4=√(-12+28)  -4 = 4 False
4: 4+2 = √(2(4)+28)  6 = √36  6=6 True
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