Difference between revisions of "Megan Homework"

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===Solve for x===
 
===Solve for x===
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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>
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4.) <math>x^4 = 16</math>
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5.) <math>\sqrt{x+2} = x</math>
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6.) <math>\sqrt{x} = -\sqrt{3}</math>
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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>
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11.) <math>\frac{\sqrt{x^2+6x}}{\sqrt{8}} = -2</math>
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12.) <math>\sqrt{(x+1)(x-5)} = 0</math>
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13.) <math>\sqrt{(x+7)(x+5)} = -2</math>

Latest revision as of 22:42, 13 April 2010

True/False

  1. [math]\sqrt{a} + \sqrt{a} = \sqrt{a+a}[/math]
  2. [math]\sqrt{8x} = 2 \sqrt{4x}[/math]
  3. [math]e^{-1/2} = -\sqrt{e}[/math]
  4. [math]x^{-2/3} = \sqrt{x^3}[/math]
  5. [math](g \cdot f)(x) = g(x)f(x) [/math]
  6. [math](g \circ f)(x) = f(g(x)) [/math]
  7. if [math]f(x) = 4x[/math] and [math]g(x) = \sqrt{x} [/math]
    1. [math](g \circ f)(x) = 4 \sqrt{x} [/math]
    2. [math](g \circ g)(y) = \sqrt[4]{y} [/math]
    3. [math](g \circ f)(z) = (f \circ g)(z) [/math]
  8. [math]t^2t^3 = t^6[/math]
  9. [math]\frac{2x+1}{x+1} = \frac{2x}{x} = 2[/math]

Simplify

  1. [math]\frac{2}{2+3\sqrt{2x}}[/math]
  2. [math]\frac{x}{x^{-2/3}}[/math]
  3. [math]r^{-1}[/math]
  4. [math]\frac{x+1}{x^2-1}[/math]

At what points are the following expressions undefined?

  1. [math]\frac{x-1}{x+1}[/math]
  2. [math]x^{-1/2}[/math]
  3. [math]\frac{6}{x^2-1}[/math]
  4. [math]\frac{2}{|x+1|-1}[/math]


Problems ||

Simplify

1.) [math]\frac{\sqrt{x}+4}{3-\sqrt{x}}[/math]

2.) [math]\frac{x^2}{\sqrt{x}+5}[/math]

3.) [math]\frac{x^2 + 2x +1}{x+1}[/math]

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]

7.) [math]y^5 y^9[/math]

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]

13.) [math]\frac{y^{-2}}{y^{-8}}[/math]


Solve for x

1.) [math]x^{1/2} = 6[/math]

2.) [math]x^{1/3} = 3[/math]

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]

8.) [math]\sqrt{x+30} = -7[/math]

9.) [math]\sqrt{x^2 - 3x -1} = 3[/math]

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]