005 Sample Final A, Question 1

Question 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.

Foundations
1) How would you find the inverse for a simpler function like $f(x)=3x+5$?
2) How are $log_{3}(x)$ and $3^{x}$ related?
Answers:
1) you would replace f(x) by y, switch x and y, and finally solve for y.
2) By stating $y=\log _{3}(x)$ we also get the following relation $x=3^{y}$

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