A sunglasses manufacturer finds that consumer demand of a certain line of sunglasses varies based on price.  Market studies predict the relationship is approximated by the function p=f(q) graphed below, where q represents the quantity of sunglasses sold in thousands and pp represents the price in dollars.

 

A) Using the graph, evaluate f(40). In a whole sentence, explain what it means in the context of this problem. Include units. 

B) Answer the following using interval notation: What is the domain of the original function? What is the range of the original function? What is the domain of the inverse function? What is the range of the inverse function?

C) Sketch a graph of the inverse function. Draw your graph on a different plot. Make sure to properly label all axes, scales and important points. Remember, these are p and q, not x and y. 

[Hint: Don\'t worry about trying to come up with piecewise formulas. Look at the coordinates of important points, and figure out where they would go on the graph of the inverse function and then play connect-the-dots] 

D) Using your graph of the inverse function, evaluate f^-1 (40). In a whole sentence, explain what it means in the context of this problem. Include units.

Transcribed Image Text:

50 s40 530 $20 $10 10 20 30 40 50 Quantity Sald (thousands of sungtasses) Price per pair (S) 50 s40 530 $20 $10 10 20 30 40 50 Quantity Sald (thousands of sungtasses) Price per pair (S)