Homework 3
Directions: Turn in your answers in class on a physical piece of paper. Staple multiple sheets together. Feel free to use Desmos for graphing.
Answer the following:
 For the curves that are actual functions in Problem 4 of Homework 2, which are onetoone?
 Suppose a function $f : \{1, 2\} \rightarrow \{1, 2\}$ is defined as such: $f(1) = 2, f(2) = 1$.
 State the domain and range of this function.
 Is this function onetoone?
 If it is onetoone, state the behavior of $f^{1}$.

Suppose $f(x)$ has domain $[1, 5]$ and range $(\infty, \infty)$. Further suppose $f(x)$ is onetoone.
 Does $f^{1}$ exist?
 If $f^{1}$ exists, what is the domain and range of $f^{1}$?
 Draw a graph of a onetoone function.
 Algebraically find the inverse of $f(x) = x$, if you can.
 Algebraically find the inverse of $f(x) = \dfrac{x + 2}{2x + 3}$, if you can.
 Algebraically find the inverse of $f(x) = \sqrt{x  3}, x \leq 12$ if you can.
 Algebraically find the inverse of $f(x) = \dfrac{(x+2)(x+1)}{(x+2)(x + 3)}$, if you can.
 Hint: The domain restriction is $\{x : x \neq 2 \text{ and } x \neq 3\}$, even if you cancel. Keep domain restrictions of the original function!
 Algebraically find the inverse of $f(x) = \dfrac{x}{x+1} + \dfrac{2x + 1}{x + 1}$, if you can.
 Suppose $f(x) = x$ and $g(x) = \dfrac{1}{x}$. Are $f(x)$ and $g(x)$ inverses? Show using the Inverse Function Property.
 Suppose $f(x) = x^2$ and $g(x) = \sqrt{x}$. Are $f(x)$ and $g(x)$ inverses? Show using the Inverse Function Property.
 Is the point $\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ on the unit circle? Show using calculations.
 What is the reference number $\bar{t}$? What is the range of values $\bar{t}$ is allowed to be?
 Find the following terminal points associated with the following $t$ values:
 $t = 0$
 $t = \frac{3\pi}{2}$
 $t = \frac{2\pi}{3}$
 $t = \frac{5\pi}{6}$
 $t = \frac{2\pi}{3}$
 $t = \frac{9\pi}{4}$
 $t = 1000\pi + \frac{2\pi}{3}$
 $t = 83\pi + \frac{\pi}{3}$
 $t = \pi + 2\pi  3\pi + \frac{4\pi}{3}$
 (skip) Find the six trigonmetric functions of $t = \frac{2\pi}{3}$.
 (skip) Find the six trigonmetric functions of $t = \frac{5\pi}{6}$.
 (skip) Why is $\tan\left(\frac{\pi}{2}\right)$ undefined?