1. Halle el dominio de las siguientes funciones: \( \begin{array}{lll}\text { a) } f(x)=\frac{1}{x-2} . & \text { b) } g(x)=\frac{x-1}{x^{2}-2} . & \text { c) } h(x)=\frac{\sqrt{x+3}}{x^{2}-2 x+1} \\ \text { 2. Hallar el dominio y rango de las siguientes funciones: } & \text { b) } f(x)=\ln (2 x+1) . & \text { c) } f(x)=e^{x^{2}}+1\end{array} \)

Suppose the half-life of a drug in the bloodstream is 9 hours. To the nearest milligram, how much of the drug is left in the bloodstream 20 hours after a 260 milligram dose? 56 milligrams 32 milligrams 190 milligrams 117 milligrams

Find the magnitude and positive direction angle of the vector \( \langle 2,-2 \sqrt{3}\rangle \). The magnitude of the vector is (Simplify your answer.)

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ \begin{array}{l}1+i\end{array} \] \( \begin{array}{l}1+i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \\ \text { (Type the value for } r \text { as an exact answer, using radicals as needed. Type the value for } \theta \text { as an integer or } \\ \text { as needed.) }\end{array} \)

Find the following product, and write the product in rectangular form, using exact values. \( \left[8\left(\cos 90^{\circ}+i \sin 90^{\circ}\right)\right]\left[3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right] \) \( \left[8\left(\cos 90^{\circ}+i \sin 90^{\circ}\right)\right]\left[3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right]=\square \) \( ( \) Type your answer in the form \( \mathrm{a}+\mathrm{bi} \).

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (-7,0) \) and \( (7,0) \); vertices at \( (3,0) \) and \( (-3,0) \)