91Ó°ÊÓ

Without using a calculator, evaluate, if possible, the following expressions. $$\sin ^{-1} \frac{\sqrt{3}}{2}$$

Let \(g(x)=x^{2}+3 .\) Find a function \(f\) that produces the given composition. $$(f \circ g)(x)=x^{4}+6 x^{2}+9$$

Use shifts and scalings to graph then 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. $$g(x)=2(x+3)^{2}$$

Assume \(\log _{b} x=0.36, \log _{b} y=0.56\), and \(\log _{b} z=0.83 .\) Evaluate the following expressions. $$\log _{b} \frac{\sqrt{x}}{\sqrt[3]{z}}$$

Use shifts and scalings to graph then 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. $$p(x)=x^{2}+3 x-5$$

Let \(g(x)=x^{2}+3 .\) Find a function \(f\) that produces the given composition. $$(f \circ g)(x)=x^{4}+6 x^{2}+20$$

Assume \(\log _{b} x=0.36, \log _{b} y=0.56\), and \(\log _{b} z=0.83 .\) Evaluate the following expressions. $$\log _{b} \frac{b^{2} x^{5 / 2}}{\sqrt{y}}$$

Use shifts and scalings to graph then 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. $$h(x)=-4 x^{2}-4 x+12$$

Let \(g(x)=x^{2}+3 .\) Find a function \(f\) that produces the given composition. $$(g \circ f)(x)=x^{4}+3$$

Without using a calculator, evaluate, if possible, the following expressions. $$\cos ^{-1}\left(-\frac{1}{2}\right)$$