Megan Homework

True/False

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

Simplify

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

At what points are the following expressions undefined?

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

Problems ||

Simplify

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

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

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

4.) [math]\displaystyle{ \frac{x^2 -10x + 25}{(x+5)(x-5)} }[/math]

5.) [math]\displaystyle{ \frac{4x^2 - y^2}{2x + y} }[/math]

6.) [math]\displaystyle{ x^2 x^7 }[/math]

7.) [math]\displaystyle{ y^5 y^9 }[/math]

8.) [math]\displaystyle{ x^5 x^{-4} }[/math]

9.) [math]\displaystyle{ x^{-2}x^{-3} }[/math]

10.) [math]\displaystyle{ \frac{x^5}{x^2} }[/math]

11.) [math]\displaystyle{ \frac{y^2}{y^{5}} }[/math]

12.) [math]\displaystyle{ \frac{y^{-3}}{y^{3}} }[/math]

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

Solve for x

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

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

3.) [math]\displaystyle{ x^3 = 125 }[/math]

4.) [math]\displaystyle{ x^4 = 16 }[/math]

5.) [math]\displaystyle{ \sqrt{x+2} = x }[/math]

6.) [math]\displaystyle{ \sqrt{x} = -\sqrt{3} }[/math]

7.) [math]\displaystyle{ \sqrt{x+1} = \sqrt{2}x }[/math]

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

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

10.) [math]\displaystyle{ \sqrt{4x^2 - 6} = \sqrt{5x} }[/math]

11.) [math]\displaystyle{ \frac{\sqrt{x^2+6x}}{\sqrt{8}} = -2 }[/math]

12.) [math]\displaystyle{ \sqrt{(x+1)(x-5)} = 0 }[/math]

13.) [math]\displaystyle{ \sqrt{(x+7)(x+5)} = -2 }[/math]