91Ó°ÊÓ

Evaluate the following expressions or state that the quantity is undefined. $$\cos ^{-1}(\cos (7 \pi / 6))$$

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

Solve the following equations. $$2^{x}=55$$

Shifting and scaling 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.)

Shifting and scaling 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. $$g(x)=-3 x^{2}$$

Using right triangles Use a right-triangle sketch to complete the following exercises. $$\text { Suppose } \theta=\cos ^{-1}(5 / 13) . \text { Find } \sin \theta \text { and } \tan \theta$$

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

Solve the following equations. $$5^{3 x}=29$$

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

Using right triangles Use a right-triangle sketch to complete the following exercises. $$\text { Suppose } \theta=\tan ^{-1}(4 / 3) . \text { Find } \sec \theta \text { and } \csc \theta$$