91Ó°ÊÓ

Find the domain of the function. $$g(x)=\sqrt[4]{x^{2}-6 x}$$

Revenue, Cost, and Profit A print shop makes bumper stickers for election campaigns. If \(x\) stickers are ordered (where \(x<10,000\) ), then the price per bumper sticker is \(0.15-0.000002 x\) dollars, and the total cost of producing the order is \(0.095 x-0.0000005 x^{2}\) dollars. Use the fact that revenue \(=\) price per item \(\times\) number of items sold to express \(R(x),\) the revenue from an order of \(x\) stickers, as a product of two functions of \(x .\)

Determine whether the equation defines \(y\) as a function of \(x .\) $$x=y^{2}$$

Revenue, Cost, and Profit A print shop makes bumper stickers for election campaigns. If \(x\) stickers are ordered (where \(x<10,000\) ), then the price per bumper sticker is \(0.15-0.000002 x\) dollars, and the total cost of producing the order is \(0.095 x-0.0000005 x^{2}\) dollars. Use the fact that profit \(=\) revenue \(-\) cost to express \(P(x),\) the profit on an order of \(x\) stickers, as a difference of two functions of \(x .\)

Find the inverse function of \(f .\) $$f(x)=1-x^{3}$$

Determine whether the equation defines \(y\) as a function of \(x .\) $$x^{2}+(y-1)^{2}=4$$

Find the domain of the function. $$g(x)=\sqrt{x^{2}-2 x-8}$$

Determine whether the equation defines \(y\) as a function of \(x .\) $$x+y^{2}=9$$

Area of a Ripple \(A\) stone is dropped in a lake, creating a circular ripple that travels outward at a speed of \(60 \mathrm{cm} / \mathrm{s}\). (IMAGE CANNOT COPY) (a) Find a function \(g\) that models the radius as a function of time. (b) Find a function \(f\) that models the area of the circle as a function of the radius. (c) Find \(f \circ g .\) What does this function represent?

A function \(f\) is given. (a) Sketch the graph of \(f .\) (b) Use the graph of \(f\) to sketch the graph of \(f^{-1}\). (c) Find \(f^{-1}\). $$f(x)=3 x-6$$