91Ó°ÊÓ

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. $$g(x)=2 x^{3}-1$$

Inverse sines and cosines Without using a calculator, evaluate the following expressions or state that the quantity is undefined. $$\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$$

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 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. $$g(x)=2(x+3)^{2}$$

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

Inverse sines and cosines Without using a calculator, evaluate the following expressions or state that the quantity is undefined. $$\sin ^{-1} \frac{\sqrt{3}}{2}$$

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

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

$$\text {Solve the following equations.}$$ $$7^{x}=21$$

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. $$h(x)=-4 x^{2}-4 x+12$$