Megan Homework

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]