91Ó°ÊÓ

Solve the following equations. $$\sin \theta \cos \theta=0,0 \leq \theta<2 \pi$$

\(\text {Let } f(x)=|x|, g(x)=x^{2}-4\), \(F(x)=\sqrt{x},\) and \(G(x)=1 /(x-2) .\) Determine the following composite functions and give their domains. $$G \circ g \circ f$$

Transformations of \(f(x)=x^{2}\) Use shifts and scalings to transform the graph of \(f(x)=x^{2}\) into the graph of \(g\). Use a graphing utility to check your work. a. \(g(x)=f(x-3)\) b. \(g(x)=f(2 x-4)\) c. \(g(x)=-3 f(x-2)+4\) d. \(g(x)=6 f\left(\frac{x-2}{3}\right)+1\)

Solve the following equations. $$\tan ^{2} 2 \theta=1,0 \leq \theta<\pi$$

\(\text {Let } f(x)=|x|, g(x)=x^{2}-4\), \(F(x)=\sqrt{x},\) and \(G(x)=1 /(x-2) .\) Determine the following composite functions and give their domains. $$F \circ g \circ g$$

$$\text {Solve the following equations.}$$ $$\ln y=3$$

?. Transformations of \(f(x)=\sqrt{x}\) Use shifts and scalings to transform the graph of \(f(x)=\sqrt{x}\) into the graph of \(g .\) Use a graphing utility to check your work. a. \(g(x)=f(x+4)\) b. \(g(x)=2 f(2 x-1)\) c. \(g(x)=\sqrt{x-1}\) d. \(g(x)=3 \sqrt{x-1}-5\)

\(\text {Let } f(x)=|x|, g(x)=x^{2}-4\), \(F(x)=\sqrt{x},\) and \(G(x)=1 /(x-2) .\) Determine the following composite functions and give their domains. $$g \circ g$$

Inverse sines and cosines Without using a calculator, evaluate the following expressions or state that the quantity is undefined. $$\sin ^{-1} 1$$

Assume \(\log _{b} x=0.36\) \(\log _{b} y=0.56,\) and \(\log _{b} z=0.83 .\) Evaluate the following expressions. $$\log _{b} \frac{x}{y}$$