Megan Homework

True/False

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

Simplify

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

At what points are the following expressions undefined?

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

Problems ||

Simplify

1.) $\frac{\sqrt{x}+4}{3-\sqrt{x}}$

2.) $\frac{x^2}{\sqrt{x}+5}$

3.) $\frac{x^2 + 2x +1}{x+1}$

4.) $\frac{x^2 -10x + 25}{(x+5)(x-5)}$

5.) $\frac{4x^2 - y^2}{2x + y}$

6.) $x^2 x^7$

7.) $y^5 y^9$

8.) $x^5 x^{-4}$

9.) $x^{-2}x^{-3}$

10.) $\frac{x^5}{x^2}$

11.) $\frac{y^2}{y^{5}}$

12.) $\frac{y^{-3}}{y^{3}}$

13.) $\frac{y^{-2}}{y^{-8}}$

Solve for x

1.) $x^{1/2} = 6$

2.) $x^{1/3} = 3$

3.) $x^3 = 125$

4.) $x^4 = 16$

5.) $\sqrt{x+2} = x$

6.) $\sqrt{x+1} = \sqrt{2}x$