91Ó°ÊÓ

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

Use shifts and scalings to graph the given functions. Then check your work with a graphing utility. Be sure to identify an original function on which the shifts and scalings are performed. \(f(x)=x^{2}-2 x+3\) (Hint: Complete the square first.)

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

Assume \(\log _{b} x=0.36\) \(\log _{b} y=0.56,\) and \(\log _{b} z=0.83 .\) Evaluate the following expressions. $$\log _{b} x^{2}$$

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

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

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

Use shifts and scalings to graph the given functions. Then check your work with a graphing utility. Be sure to identify an original function on which the shifts and scalings are performed. $$g(x)=-3 x^{2}$$

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

Let \(g(x)=x^{2}+3 .\) Find a function \(f\) that produces the given composition. $$(f \circ g)(x)=\frac{1}{x^{2}+3}$$