Difference between revisions of "Megan Homework"

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(Created page with '===True/False=== #<math>\sqrt{a} + \sqrt{a} = \sqrt{a+a}</math> #<math>\sqrt{8x} = 2 \sqrt{4x}</math>')
 
 
(18 intermediate revisions by the same user not shown)
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#<math>\sqrt{a} + \sqrt{a} = \sqrt{a+a}</math>
 
#<math>\sqrt{a} + \sqrt{a} = \sqrt{a+a}</math>
 
#<math>\sqrt{8x} = 2 \sqrt{4x}</math>
 
#<math>\sqrt{8x} = 2 \sqrt{4x}</math>
 +
#<math>e^{-1/2} = -\sqrt{e}</math>
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#<math>x^{-2/3} = \sqrt{x^3}</math>
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# <math>(g \cdot f)(x) = g(x)f(x) </math>
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# <math>(g \circ f)(x) = f(g(x)) </math>
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#if <math>f(x) = 4x</math> and <math>g(x) = \sqrt{x} </math>
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## <math>(g \circ f)(x) = 4 \sqrt{x} </math>
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## <math>(g \circ g)(y) = \sqrt[4]{y} </math>
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## <math>(g \circ f)(z) = (f \circ g)(z) </math>
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#<math>t^2t^3 = t^6</math>
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#<math>\frac{2x+1}{x+1} = \frac{2x}{x} = 2</math>
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 +
===Simplify===
 +
#<math>\frac{2}{2+3\sqrt{2x}}</math>
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#<math>\frac{x}{x^{-2/3}}</math>
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#<math>r^{-1}</math>
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#<math>\frac{x+1}{x^2-1}</math>
 +
 +
===At what points are the following expressions undefined?===
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#<math>\frac{x-1}{x+1}</math>
 +
#<math>x^{-1/2}</math>
 +
#<math>\frac{6}{x^2-1}</math>
 +
#<math>\frac{2}{|x+1|-1}</math>
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 +
 +
==Problems ||==
 +
 +
===Simplify===
 +
 +
1.) <math>\frac{\sqrt{x}+4}{3-\sqrt{x}}</math>
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 +
2.) <math>\frac{x^2}{\sqrt{x}+5}</math>
 +
 +
3.) <math>\frac{x^2 + 2x +1}{x+1}</math>
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 +
4.) <math>\frac{x^2 -10x + 25}{(x+5)(x-5)}</math>
 +
 +
5.) <math>\frac{4x^2 - y^2}{2x + y}</math>
 +
 +
 +
6.) <math>x^2 x^7</math>
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 +
7.) <math>y^5 y^9</math>
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8.) <math>x^5 x^{-4}</math>
 +
 +
9.) <math>x^{-2}x^{-3}</math>
 +
 +
 +
10.) <math>\frac{x^5}{x^2}</math>
 +
 +
11.) <math>\frac{y^2}{y^{5}}</math>
 +
 +
12.) <math>\frac{y^{-3}}{y^{3}}</math>
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 +
13.) <math>\frac{y^{-2}}{y^{-8}}</math>
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 +
 +
===Solve for x===
 +
 +
1.) <math>x^{1/2} = 6</math>
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 +
2.) <math>x^{1/3} = 3</math>
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 +
3.) <math>x^3 = 125</math>
 +
 +
4.) <math>x^4 = 16</math>
 +
 +
 +
5.) <math>\sqrt{x+2} = x</math>
 +
 +
6.) <math>\sqrt{x} = -\sqrt{3}</math>
 +
 +
7.) <math>\sqrt{x+1} = \sqrt{2}x</math>
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 +
8.) <math>\sqrt{x+30} = -7</math>
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 +
9.) <math>\sqrt{x^2 - 3x -1} = 3</math>
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 +
10.) <math>\sqrt{4x^2 - 6} = \sqrt{5x}</math>
 +
 +
11.) <math>\frac{\sqrt{x^2+6x}}{\sqrt{8}} = -2</math>
 +
 +
12.) <math>\sqrt{(x+1)(x-5)} = 0</math>
 +
 +
13.) <math>\sqrt{(x+7)(x+5)} = -2</math>

Latest revision as of 22:42, 13 April 2010

True/False

  1. √a+√a=√a+a
  2. √8x=2√4x
  3. e−1/2=−√e
  4. x−2/3=√x3
  5. (g⋅f)(x)=g(x)f(x)
  6. (g∘f)(x)=f(g(x))
  7. if f(x)=4x and g(x)=√x
    1. (g∘f)(x)=4√x
    2. (g∘g)(y)=4√y
    3. (g∘f)(z)=(f∘g)(z)
  8. t2t3=t6
  9. 2x+1x+1=2xx=2

Simplify

  1. 22+3√2x
  2. xx−2/3
  3. r−1
  4. x+1x2−1

At what points are the following expressions undefined?

  1. x−1x+1
  2. x−1/2
  3. 6x2−1
  4. 2|x+1|−1


Problems ||

Simplify

1.) √x+43−√x

2.) x2√x+5

3.) x2+2x+1x+1

4.) x2−10x+25(x+5)(x−5)

5.) 4x2−y22x+y


6.) x2x7

7.) y5y9

8.) x5x−4

9.) x−2x−3


10.) x5x2

11.) y2y5

12.) y−3y3

13.) y−2y−8


Solve for x

1.) x1/2=6

2.) x1/3=3

3.) x3=125

4.) x4=16


5.) √x+2=x

6.) √x=−√3

7.) √x+1=√2x

8.) √x+30=−7

9.) √x2−3x−1=3

10.) √4x2−6=√5x

11.) √x2+6x√8=−2

12.) √(x+1)(x−5)=0

13.) √(x+7)(x+5)=−2

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