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]

Simplify

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

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