5F13Final

1. Please circle either true or false,
    a. (True/False)In a geometric sequence, the common ratio is always positive.
    b. (True/False) A linear system of equations always has a solution.
    c. (True/False) Every function has an inverse.
    d. (True/False) Trigonometric equations do not always have unique solutions.
    e. (True/False) The domain of $f(x)=\tan ^{-1}(x)$ is all real numbers.
    f. (True/False) The function $\log _{a}(x)$ is defined for all real numbers.

2.Find the domain of the following function. Your answer should be in interval notation $f(x)={\frac {1}{\sqrt {x^{2}-x-2}}}$

3. Find f $\circ$ g and its domain if $f(x)=x^{2}+1\qquad g(x)={\sqrt {x-1}}$

4. Find the inverse of the following function $f(x)={\frac {3x}{2x-1}}$

5. Solve the following inequality. Your answer should be in interval notation. ${\frac {3x+5}{x+2}}\geq 2$

6. Factor the following polynomial completely,     $p(x)=x^{4}+x^{3}+2x-4$

7. Solve the following equation,      $2\log _{5}(x)=3\log _{5}(4)$

8. Solve the following equation,      $3^{2x}+3^{x}-2=0$

9. Solve the following system of equations

${\begin{matrix}2x&+&3y&=&1\\-x&+&y&=&-3\end{matrix}}$